diff --git a/mypy/semanal.py b/mypy/semanal.py
index 219459c92e3c..123e5a0ca0fc 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -309,7 +309,7 @@
 )
 from mypy.types_utils import is_invalid_recursive_alias, store_argument_type
 from mypy.typevars import fill_typevars
-from mypy.util import correct_relative_import, is_dunder, module_prefix, unmangle, unnamed_function
+from mypy.util import correct_relative_import, module_prefix, unmangle, unnamed_function
 from mypy.visitor import NodeVisitor
 
 T = TypeVar("T")
@@ -3841,9 +3841,13 @@ def store_final_status(self, s: AssignmentStmt) -> None:
                         and isinstance(cur_node.node, Var)
                         and not (isinstance(s.rvalue, TempNode) and s.rvalue.no_rhs)
                     ):
-                        # Double underscored members are writable on an `Enum`.
+                        # Double underscored names are writable on an `Enum`:
+                        # - Dunders (__x__) are not enum members
+                        # - Private names (__x) are not enum members (since Python 3.11)
                         # (Except read-only `__members__` but that is handled in type checker)
-                        cur_node.node.is_final = s.is_final_def = not is_dunder(cur_node.node.name)
+                        cur_node.node.is_final = s.is_final_def = (
+                            not cur_node.node.name.startswith("__")
+                        )
 
                 # Special case: deferred initialization of a final attribute in __init__.
                 # In this case we just pretend this is a valid final definition to suppress
diff --git a/test-data/unit/check-enum.test b/test-data/unit/check-enum.test
index c05dfdef2bf7..15a0b80c3341 100644
--- a/test-data/unit/check-enum.test
+++ b/test-data/unit/check-enum.test
@@ -1602,6 +1602,20 @@ Medal.silver = 2  # E: Cannot assign to final attribute "silver"
 [builtins fixtures/enum.pyi]
 
 
+[case testEnumPrivateNameNotFinal]
+# Private names (__x) are not enum members and should not be final
+from enum import Enum
+
+class MyEnum(Enum):
+    __config = "some_value"
+    A = 1
+    B = 2
+
+# __config is not a member so reassignment should be allowed
+MyEnum._MyEnum__config = "other_value"
+[builtins fixtures/enum.pyi]
+
+
 [case testEnumFinalValuesCannotRedefineValueProp]
 from enum import Enum
 class Types(Enum):