diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index b3f5fb6f0291a..d180945d85d00 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -9,6 +9,7 @@
     FrozenSet,
     Hashable,
     List,
+    NewType,
     Optional,
     Sequence,
     Tuple,
@@ -139,7 +140,9 @@ def index_arithmetic_method(self, other):
 
 
 _o_dtype = np.dtype(object)
-_Identity = object
+
+
+_Identity = NewType("_Identity", object)
 
 
 def _new_Index(cls, d):
@@ -238,7 +241,7 @@ def _outer_indexer(self, left, right):
 
     _typ = "index"
     _data: Union[ExtensionArray, np.ndarray]
-    _id = None
+    _id: _Identity
     _name: Label = None
     # MultiIndex.levels previously allowed setting the index name. We
     # don't allow this anymore, and raise if it happens rather than
@@ -453,8 +456,9 @@ def _simple_new(cls, values, name: Label = None):
         result._index_data = values
         result._name = name
         result._cache = {}
+        result._reset_identity()
 
-        return result._reset_identity()
+        return result
 
     @cache_readonly
     def _constructor(self):
@@ -558,15 +562,16 @@ def is_(self, other) -> bool:
         --------
         Index.identical : Works like ``Index.is_`` but also checks metadata.
         """
-        # use something other than None to be clearer
-        return self._id is getattr(other, "_id", Ellipsis) and self._id is not None
+        try:
+            return self._id is other._id
+        except AttributeError:
+            return False
 
-    def _reset_identity(self):
+    def _reset_identity(self) -> None:
         """
         Initializes or resets ``_id`` attribute with new object.
         """
-        self._id = _Identity()
-        return self
+        self._id = _Identity(object())
 
     def _cleanup(self):
         self._engine.clear_mapping()
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 2ce4538a63d25..38a0d18ac732d 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -316,7 +316,9 @@ def __new__(
             new_codes = result._verify_integrity()
             result._codes = new_codes
 
-        return result._reset_identity()
+        result._reset_identity()
+
+        return result
 
     def _validate_codes(self, level: List, code: List):
         """
diff --git a/pandas/tests/arithmetic/test_object.py b/pandas/tests/arithmetic/test_object.py
index 02cb4f4d7a606..e0c03f28f7af5 100644
--- a/pandas/tests/arithmetic/test_object.py
+++ b/pandas/tests/arithmetic/test_object.py
@@ -343,8 +343,9 @@ def _simple_new(cls, values, name=None, dtype=None):
         result._index_data = values
         result._name = name
         result._calls = 0
+        result._reset_identity()
 
-        return result._reset_identity()
+        return result
 
     def __add__(self, other):
         self._calls += 1