diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index c1b73c60be92b..af61354470a71 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -14,7 +14,7 @@ including other versions of pandas.
 
 Fixed regressions
 ~~~~~~~~~~~~~~~~~
-
+- Regression in :meth:`DatetimeIndex.intersection` incorrectly raising ``AssertionError`` when intersecting against a list (:issue:`35876`)
 -
 -
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 6d9d75a69e91d..9d00f50a65a06 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -704,16 +704,16 @@ def intersection(self, other, sort=False):
                 if result.freq is None:
                     # TODO: no tests rely on this; needed?
                     result = result._with_freq("infer")
-            assert result.name == res_name
+            result.name = res_name
             return result
 
         elif not self._can_fast_intersect(other):
             result = Index.intersection(self, other, sort=sort)
-            assert result.name == res_name
             # We need to invalidate the freq because Index.intersection
             #  uses _shallow_copy on a view of self._data, which will preserve
             #  self.freq if we're not careful.
             result = result._with_freq(None)._with_freq("infer")
+            result.name = res_name
             return result
 
         # to make our life easier, "sort" the two ranges
diff --git a/pandas/tests/indexes/datetimes/test_setops.py b/pandas/tests/indexes/datetimes/test_setops.py
index 6670b079ddd29..f19e78323ab23 100644
--- a/pandas/tests/indexes/datetimes/test_setops.py
+++ b/pandas/tests/indexes/datetimes/test_setops.py
@@ -470,6 +470,13 @@ def test_intersection_bug(self):
         tm.assert_index_equal(result, b)
         assert result.freq == b.freq
 
+    def test_intersection_list(self):
+        # GH#35876
+        values = [pd.Timestamp("2020-01-01"), pd.Timestamp("2020-02-01")]
+        idx = pd.DatetimeIndex(values, name="a")
+        res = idx.intersection(values)
+        tm.assert_index_equal(res, idx)
+
     def test_month_range_union_tz_pytz(self, sort):
         from pytz import timezone