Fixed job name bug

src/BenchmarkDotNet/Characteristics/CharacteristicObject.cs

@@ -402,6 +402,12 @@ protected CharacteristicObject UnfreezeCopyCore()
             var newRoot = (CharacteristicObject)Activator.CreateInstance(GetType());
             newRoot.ApplyCore(this);
 
+            // Preserve the IdCharacteristic of the original object
+            if (this.HasValue(IdCharacteristic))
+            {
+                newRoot.SetValue(IdCharacteristic, this.GetValue(IdCharacteristic));
+            }
+
             return newRoot;
         }
         #endregion

tests/BenchmarkDotNet.Tests/Configs/JobTests.cs

@@ -474,6 +474,20 @@ public static void WithNuGet()
             Assert.Equal(expected, j.Infrastructure.NuGetReferences); // ensure that the list's equality operator returns true when the contents are the same
         }
 
+        [Fact]
+        public static void UnfreezeCopy_PreservesIdCharacteristic()
+        {
+            // Arrange
+            var original = new Job();
+            original.SetValue(Job.IdCharacteristic, "TestID");
+
+            // Act
+            var copy = original.UnfreezeCopy();
+
+            // Assert
+            Assert.Equal("TestID", copy.GetValue(Job.IdCharacteristic));
+        }
+
         private static bool IsSubclassOfobModeOfItself(Type type)
         {
             Type jobModeOfT;