diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index 123dfa07f4331..18a431cc2be5e 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -17,6 +17,7 @@ Fixed regressions
 
 - Fixed regression in :meth:`DataFrame.to_excel` when ``columns`` kwarg is passed (:issue:`31677`)
 - Fixed regression in :meth:`Series.align` when ``other`` is a DataFrame and ``method`` is not None (:issue:`31785`)
+- Fixed regression in :meth:`groupby(..).agg() <pandas.core.groupby.GroupBy.agg>` which was failing on frames with MultiIndex columns and a custom function (:issue:`31777`)
 - Fixed regression in ``groupby(..).rolling(..).apply()`` (``RollingGroupby``) where the ``raw`` parameter was ignored (:issue:`31754`)
 - Fixed regression in :meth:`rolling(..).corr() <pandas.core.window.rolling.Rolling.corr>` when using a time offset (:issue:`31789`)
 - Fixed regression in :meth:`groupby(..).nunique() <pandas.core.groupby.DataFrameGroupBy.nunique>` which was modifying the original values if ``NaN`` values were present (:issue:`31950`)
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index b7ac3048631c5..fda66f68f7adc 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -955,9 +955,11 @@ def aggregate(self, func=None, *args, **kwargs):
                         raise
                     result = self._aggregate_frame(func)
                 else:
-                    result.columns = Index(
-                        result.columns.levels[0], name=self._selected_obj.columns.name
-                    )
+                    # select everything except for the last level, which is the one
+                    # containing the name of the function(s), see GH 32040
+                    result.columns = result.columns.rename(
+                        [self._selected_obj.columns.name] * result.columns.nlevels
+                    ).droplevel(-1)
 
         if not self.as_index:
             self._insert_inaxis_grouper_inplace(result)
diff --git a/pandas/tests/groupby/aggregate/test_aggregate.py b/pandas/tests/groupby/aggregate/test_aggregate.py
index 48f8de7e51ae4..1265547653d7b 100644
--- a/pandas/tests/groupby/aggregate/test_aggregate.py
+++ b/pandas/tests/groupby/aggregate/test_aggregate.py
@@ -691,6 +691,19 @@ def test_agg_relabel_multiindex_duplicates():
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "func", [lambda s: s.mean(), lambda s: np.mean(s), lambda s: np.nanmean(s)]
+)
+def test_multiindex_custom_func(func):
+    # GH 31777
+    data = [[1, 4, 2], [5, 7, 1]]
+    df = pd.DataFrame(data, columns=pd.MultiIndex.from_arrays([[1, 1, 2], [3, 4, 3]]))
+    result = df.groupby(np.array([0, 1])).agg(func)
+    expected_dict = {(1, 3): {0: 1, 1: 5}, (1, 4): {0: 4, 1: 7}, (2, 3): {0: 2, 1: 1}}
+    expected = pd.DataFrame(expected_dict)
+    tm.assert_frame_equal(result, expected)
+
+
 def myfunc(s):
     return np.percentile(s, q=0.90)