diff --git a/crates/oxc_minifier/src/compressor.rs b/crates/oxc_minifier/src/compressor.rs
index 2f2cc96f83cf5..8f198d95ea32d 100644
--- a/crates/oxc_minifier/src/compressor.rs
+++ b/crates/oxc_minifier/src/compressor.rs
@@ -31,7 +31,8 @@ impl<'a> Compressor<'a> {
         let normalize_options =
             NormalizeOptions { convert_while_to_fors: true, convert_const_to_let: true };
         Normalize::new(normalize_options, self.options).build(program, &mut ctx);
-        PeepholeOptimizations::new(self.options.target).run_in_loop(program, &mut ctx);
+        PeepholeOptimizations::new(self.options.target, self.options.keep_names)
+            .run_in_loop(program, &mut ctx);
         LatePeepholeOptimizations::new(self.options.target).build(program, &mut ctx);
     }
 
diff --git a/crates/oxc_minifier/src/lib.rs b/crates/oxc_minifier/src/lib.rs
index d18b94bf28a8a..0837a7d908cdf 100644
--- a/crates/oxc_minifier/src/lib.rs
+++ b/crates/oxc_minifier/src/lib.rs
@@ -18,7 +18,9 @@ use oxc_semantic::{Scoping, SemanticBuilder, Stats};
 
 pub use oxc_mangler::MangleOptions;
 
-pub use crate::{compressor::Compressor, options::CompressOptions};
+pub use crate::{
+    compressor::Compressor, options::CompressOptions, options::CompressOptionsKeepNames,
+};
 
 #[derive(Debug, Clone, Copy)]
 pub struct MinifierOptions {
diff --git a/crates/oxc_minifier/src/options.rs b/crates/oxc_minifier/src/options.rs
index 79feec1d22369..abdb5aa80d2c4 100644
--- a/crates/oxc_minifier/src/options.rs
+++ b/crates/oxc_minifier/src/options.rs
@@ -12,6 +12,9 @@ pub struct CompressOptions {
     /// Default `ESTarget::ESNext`
     pub target: ESTarget,
 
+    /// Keep function / class names.
+    pub keep_names: CompressOptionsKeepNames,
+
     /// Remove `debugger;` statements.
     ///
     /// Default `true`
@@ -32,10 +35,55 @@ impl Default for CompressOptions {
 
 impl CompressOptions {
     pub fn smallest() -> Self {
-        Self { target: ESTarget::ESNext, drop_debugger: true, drop_console: true }
+        Self {
+            target: ESTarget::ESNext,
+            keep_names: CompressOptionsKeepNames::all_false(),
+            drop_debugger: true,
+            drop_console: true,
+        }
     }
 
     pub fn safest() -> Self {
-        Self { target: ESTarget::ESNext, drop_debugger: false, drop_console: false }
+        Self {
+            target: ESTarget::ESNext,
+            keep_names: CompressOptionsKeepNames::all_true(),
+            drop_debugger: false,
+            drop_console: false,
+        }
+    }
+}
+
+#[derive(Debug, Clone, Copy, Default)]
+pub struct CompressOptionsKeepNames {
+    /// Keep function names so that `Function.prototype.name` is preserved.
+    ///
+    /// This does not guarantee that the `undefined` name is preserved.
+    ///
+    /// Default `false`
+    pub function: bool,
+
+    /// Keep class names so that `Class.prototype.name` is preserved.
+    ///
+    /// This does not guarantee that the `undefined` name is preserved.
+    ///
+    /// Default `false`
+    pub class: bool,
+}
+
+impl CompressOptionsKeepNames {
+    pub fn all_false() -> Self {
+        Self { function: false, class: false }
+    }
+
+    pub fn all_true() -> Self {
+        Self { function: true, class: true }
+    }
+
+    pub fn function_only() -> Self {
+        Self { function: true, class: false }
+    }
+
+    pub fn class_only() -> Self {
+        Self { function: false, class: true }
     }
 }
diff --git a/crates/oxc_minifier/src/peephole/minimize_conditional_expression.rs b/crates/oxc_minifier/src/peephole/minimize_conditional_expression.rs
index 33af746a3e8e6..b96cf4b15e1ad 100644
--- a/crates/oxc_minifier/src/peephole/minimize_conditional_expression.rs
+++ b/crates/oxc_minifier/src/peephole/minimize_conditional_expression.rs
@@ -423,10 +423,11 @@ impl<'a> PeepholeOptimizations {
         if !matches!(consequent.left, AssignmentTarget::AssignmentTargetIdentifier(_)) {
             return None;
         }
-        // TODO: need this condition when `keep_fnames` is introduced
-        // if consequent.right.is_anonymous_function_definition() {
-        //     return None;
-        // }
+        // NOTE: if the right hand side is an anonymous function, applying this compression will
+        // set the `name` property of that function.
+        // Since codes relying on the fact that function's name is undefined should be rare,
+        // we do this compression even if `keep_names` is enabled.
+
         if consequent.operator != AssignmentOperator::Assign
             || consequent.operator != alternate.operator
             || consequent.left.content_ne(&alternate.left)
diff --git a/crates/oxc_minifier/src/peephole/minimize_conditions.rs b/crates/oxc_minifier/src/peephole/minimize_conditions.rs
index d4a373a155c37..b67b344d100ff 100644
--- a/crates/oxc_minifier/src/peephole/minimize_conditions.rs
+++ b/crates/oxc_minifier/src/peephole/minimize_conditions.rs
@@ -187,7 +187,10 @@ impl<'a> PeepholeOptimizations {
         }
 
         let Expression::LogicalExpression(logical_expr) = &mut expr.right else { return false };
-        let new_op = logical_expr.operator.to_assignment_operator();
+        // NOTE: if the right hand side is an anonymous function, applying this compression will
+        // set the `name` property of that function.
+        // Since codes relying on the fact that function's name is undefined should be rare,
+        // we do this compression even if `keep_names` is enabled.
 
         let (
             AssignmentTarget::AssignmentTargetIdentifier(write_id_ref),
@@ -202,6 +205,7 @@ impl<'a> PeepholeOptimizations {
             return false;
         }
 
+        let new_op = logical_expr.operator.to_assignment_operator();
         expr.operator = new_op;
         expr.right = ctx.ast.move_expression(&mut logical_expr.right);
         true
@@ -1317,11 +1321,8 @@ mod test {
 
         // a.b might have a side effect
         test_same("x ? a.b = 0 : a.b = 1");
-        // `a = x ? () => 'a' : () => 'b'` does not set the name property of the function
-        // TODO: need to pass these tests when `keep_fnames` are introduced
-        // test_same("x ? a = () => 'a' : a = () => 'b'");
-        // test_same("x ? a = function () { return 'a' } : a = function () { return 'b' }");
-        // test_same("x ? a = class { foo = 'a' } : a = class { foo = 'b' }");
+        // `a = x ? () => 'a' : () => 'b'` does not set the name property of the function, but we ignore that difference
+        test("x ? a = () => 'a' : a = () => 'b'", "a = x ? () => 'a' : () => 'b'");
 
         // for non `=` operators, `GetValue(lref)` is called before `Evaluation of AssignmentExpression`
         // so cannot be fold to `a += x ? 0 : 1`
@@ -1376,7 +1377,7 @@ mod test {
         test("x && (x = g())", "x &&= g()");
         test("x ?? (x = g())", "x ??= g()");
 
-        // `||=`, `&&=`, `??=` sets the name property of the function
+        // `||=`, `&&=`, `??=` sets the name property of the function, but we ignore that difference
         // Example case: `let f = false; f || (f = () => {}); console.log(f.name)`
         test("x || (x = () => 'a')", "x ||= () => 'a'");
 
@@ -1424,6 +1425,11 @@ mod test {
         // This case is not supported, since the minifier does not support with statements
         // test_same("var x; with (z) { x = x || 1 }");
 
+        // `||=`, `&&=`, `??=` sets the name property of the function, while `= x || y` does not
+        // but we ignore that difference
+        // Example case: `let f = false; f = f || (() => {}); console.log(f.name)`
+        test("var x; x = x || (() => 'a')", "var x; x ||= (() => 'a')");
+
         let target = ESTarget::ES2019;
         let code = "var x; x = x || 1";
         assert_eq!(
diff --git a/crates/oxc_minifier/src/peephole/mod.rs b/crates/oxc_minifier/src/peephole/mod.rs
index 37f77aa604ea8..ddfe59a8fc82b 100644
--- a/crates/oxc_minifier/src/peephole/mod.rs
+++ b/crates/oxc_minifier/src/peephole/mod.rs
@@ -25,12 +25,13 @@ use oxc_data_structures::stack::NonEmptyStack;
 use oxc_syntax::{es_target::ESTarget, scope::ScopeId};
 use oxc_traverse::{ReusableTraverseCtx, Traverse, TraverseCtx, traverse_mut_with_ctx};
 
-use crate::ctx::Ctx;
+use crate::{ctx::Ctx, options::CompressOptionsKeepNames};
 
 pub use self::normalize::{Normalize, NormalizeOptions};
 
 pub struct PeepholeOptimizations {
     target: ESTarget,
+    keep_names: CompressOptionsKeepNames,
 
     /// Walk the ast in a fixed point loop until no changes are made.
     /// `prev_function_changed`, `functions_changed` and `current_function` track changes
@@ -45,9 +46,10 @@ pub struct PeepholeOptimizations {
 }
 
 impl<'a> PeepholeOptimizations {
-    pub fn new(target: ESTarget) -> Self {
+    pub fn new(target: ESTarget, keep_names: CompressOptionsKeepNames) -> Self {
         Self {
             target,
+            keep_names,
             iteration: 0,
             prev_functions_changed: FxHashSet::default(),
             functions_changed: FxHashSet::default(),
@@ -363,7 +365,12 @@ pub struct DeadCodeElimination {
 
 impl<'a> DeadCodeElimination {
     pub fn new() -> Self {
-        Self { inner: PeepholeOptimizations::new(ESTarget::ESNext) }
+        Self {
+            inner: PeepholeOptimizations::new(
+                ESTarget::ESNext,
+                CompressOptionsKeepNames::all_true(),
+            ),
+        }
     }
 
     pub fn build(&mut self, program: &mut Program<'a>, ctx: &mut ReusableTraverseCtx<'a>) {
diff --git a/crates/oxc_minifier/src/peephole/substitute_alternate_syntax.rs b/crates/oxc_minifier/src/peephole/substitute_alternate_syntax.rs
index 9231172f61f21..95eef6eb0349f 100644
--- a/crates/oxc_minifier/src/peephole/substitute_alternate_syntax.rs
+++ b/crates/oxc_minifier/src/peephole/substitute_alternate_syntax.rs
@@ -971,6 +971,10 @@ impl<'a> PeepholeOptimizations {
     ///
     /// This compression is not safe if the code relies on `Function::name`.
     fn try_remove_name_from_functions(&mut self, func: &mut Function<'a>, ctx: Ctx<'a, '_>) {
+        if self.keep_names.function {
+            return;
+        }
+
         if func.id.as_ref().is_some_and(|id| !ctx.scoping().symbol_is_used(id.symbol_id())) {
             func.id = None;
             self.mark_current_function_as_changed();
@@ -981,8 +985,12 @@ impl<'a> PeepholeOptimizations {
     ///
     /// e.g. `var a = class C {}` -> `var a = class {}`
     ///
-    /// This compression is not safe if the code relies on `Function::name`.
+    /// This compression is not safe if the code relies on `Class::name`.
     fn try_remove_name_from_classes(&mut self, class: &mut Class<'a>, ctx: Ctx<'a, '_>) {
+        if self.keep_names.class {
+            return;
+        }
+
         if class.id.as_ref().is_some_and(|id| !ctx.scoping().symbol_is_used(id.symbol_id())) {
             class.id = None;
             self.mark_current_function_as_changed();
@@ -1206,9 +1214,16 @@ mod test {
 
     use crate::{
         CompressOptions,
+        options::CompressOptionsKeepNames,
         tester::{run, test, test_same},
     };
 
+    fn test_same_keep_names(keep_names: CompressOptionsKeepNames, code: &str) {
+        let result = run(code, Some(CompressOptions { keep_names, ..CompressOptions::smallest() }));
+        let expected = run(code, None);
+        assert_eq!(result, expected, "\nfor source\n{code}\ngot\n{result}");
+    }
+
     #[test]
     fn test_fold_return_result() {
         test("function f(){return !1;}", "function f(){return !1}");
@@ -1858,8 +1873,10 @@ mod test {
     fn test_remove_name_from_expressions() {
         test("var a = function f() {}", "var a = function () {}");
         test_same("var a = function f() { return f; }");
+        test_same_keep_names(CompressOptionsKeepNames::function_only(), "var a = function f() {}");
         test("var a = class C {}", "var a = class {}");
         test_same("var a = class C { foo() { return C } }");
+        test_same_keep_names(CompressOptionsKeepNames::class_only(), "var a = class C {}");
     }
 
     #[test]
diff --git a/crates/oxc_minifier/tests/peephole/mod.rs b/crates/oxc_minifier/tests/peephole/mod.rs
index 8c5383affced3..21edb9b416949 100644
--- a/crates/oxc_minifier/tests/peephole/mod.rs
+++ b/crates/oxc_minifier/tests/peephole/mod.rs
@@ -4,7 +4,7 @@ mod esbuild;
 use oxc_minifier::CompressOptions;
 
 fn test(source_text: &str, expected: &str) {
-    let options = CompressOptions::safest();
+    let options = CompressOptions { drop_debugger: false, ..CompressOptions::default() };
     crate::test(source_text, expected, options);
 }
 
diff --git a/napi/minify/index.d.ts b/napi/minify/index.d.ts
index 16b90c18cb776..8daf831a49737 100644
--- a/napi/minify/index.d.ts
+++ b/napi/minify/index.d.ts
@@ -23,6 +23,8 @@ export interface CompressOptions {
    * @default 'esnext'
    */
   target?: 'esnext' | 'es2015' | 'es2016' | 'es2017' | 'es2018' | 'es2019' | 'es2020' | 'es2021' | 'es2022' | 'es2023' | 'es2024'
+  /** Keep function / class names. */
+  keepNames?: CompressOptionsKeepNames
   /**
    * Pass true to discard calls to `console.*`.
    *
@@ -37,6 +39,25 @@ export interface CompressOptions {
   dropDebugger?: boolean
 }
 
+export interface CompressOptionsKeepNames {
+  /**
+   * Keep function names so that `Function.prototype.name` is preserved.
+   *
+   * This does not guarantee that the `undefined` name is preserved.
+   *
+   * @default false
+   */
+  function: boolean
+  /**
+   * Keep class names so that `Class.prototype.name` is preserved.
+   *
+   * This does not guarantee that the `undefined` name is preserved.
+   *
+   * @default false
+   */
+  class: boolean
+}
+
 export interface MangleOptions {
   /**
    * Pass `true` to mangle names declared in the top level scope.
diff --git a/napi/minify/src/options.rs b/napi/minify/src/options.rs
index e26b4b0c6965d..ff2ddb3fe753f 100644
--- a/napi/minify/src/options.rs
+++ b/napi/minify/src/options.rs
@@ -23,6 +23,9 @@ pub struct CompressOptions {
     )]
     pub target: Option<String>,
 
+    /// Keep function / class names.
+    pub keep_names: Option<CompressOptionsKeepNames>,
+
     /// Pass true to discard calls to `console.*`.
     ///
     /// @default false
@@ -36,7 +39,7 @@ pub struct CompressOptions {
 
 impl Default for CompressOptions {
     fn default() -> Self {
-        Self { target: None, drop_console: None, drop_debugger: Some(true) }
+        Self { target: None, keep_names: None, drop_console: None, drop_debugger: Some(true) }
     }
 }
 
@@ -51,12 +54,36 @@ impl TryFrom<&CompressOptions> for oxc_minifier::CompressOptions {
                 .map(|s| ESTarget::from_str(s))
                 .transpose()?
                 .unwrap_or(default.target),
+            keep_names: o.keep_names.as_ref().map(Into::into).unwrap_or_default(),
             drop_console: o.drop_console.unwrap_or(default.drop_console),
             drop_debugger: o.drop_debugger.unwrap_or(default.drop_debugger),
         })
     }
 }
 
+#[napi(object)]
+pub struct CompressOptionsKeepNames {
+    /// Keep function names so that `Function.prototype.name` is preserved.
+    ///
+    /// This does not guarantee that the `undefined` name is preserved.
+    ///
+    /// @default false
+    pub function: bool,
+
+    /// Keep class names so that `Class.prototype.name` is preserved.
+    ///
+    /// This does not guarantee that the `undefined` name is preserved.
+    ///
+    /// @default false
+    pub class: bool,
+}
+
+impl From<&CompressOptionsKeepNames> for oxc_minifier::CompressOptionsKeepNames {
+    fn from(o: &CompressOptionsKeepNames) -> Self {
+        oxc_minifier::CompressOptionsKeepNames { function: o.function, class: o.class }
+    }
+}
+
 #[napi(object)]
 #[derive(Default)]
 pub struct MangleOptions {
diff --git a/napi/playground/src/lib.rs b/napi/playground/src/lib.rs
index b4c6e785cc33f..a8d0c020da754 100644
--- a/napi/playground/src/lib.rs
+++ b/napi/playground/src/lib.rs
@@ -266,10 +266,10 @@ impl Oxc {
                     CompressOptions {
                         drop_console: compress_options.drop_console,
                         drop_debugger: compress_options.drop_debugger,
-                        ..CompressOptions::safest()
+                        ..CompressOptions::default()
                     }
                 } else {
-                    CompressOptions::safest()
+                    CompressOptions::default()
                 }),
             };
             Minifier::new(options).build(&allocator, &mut program).scoping