diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 812af544ed9d8..e00fd2d3bbe04 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -512,6 +512,7 @@ Reshaping
 - Bug in func :meth:`crosstab` when using multiple columns with ``margins=True`` and ``normalize=True`` (:issue:`35144`)
 - Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 - Bug in :meth:`Series.transform` would give incorrect results or raise when the argument ``func`` was dictionary (:issue:`35811`)
+- Bug in :meth:`DataFrame.pivot` did not preserve :class:`MultiIndex` level names for columns when rows and columns both multiindexed (:issue:`36360`)
 - Bug in :func:`join` returned a non deterministic level-order for the resulting :class:`MultiIndex` (:issue:`36910`)
 -
 
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 9c78166ce0480..505435be9127c 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -1645,8 +1645,8 @@ def _wrap_aggregated_output(
         DataFrame
         """
         indexed_output = {key.position: val for key, val in output.items()}
-        name = self._obj_with_exclusions._get_axis(1 - self.axis).name
-        columns = Index([key.label for key in output], name=name)
+        columns = Index([key.label for key in output])
+        columns._set_names(self._obj_with_exclusions._get_axis(1 - self.axis).names)
 
         result = self.obj._constructor(indexed_output)
         result.columns = columns
diff --git a/pandas/tests/reshape/test_pivot_multilevel.py b/pandas/tests/reshape/test_pivot_multilevel.py
index 8374e829e6a28..f59a469c05d15 100644
--- a/pandas/tests/reshape/test_pivot_multilevel.py
+++ b/pandas/tests/reshape/test_pivot_multilevel.py
@@ -2,7 +2,7 @@
 import pytest
 
 import pandas as pd
-from pandas import Index, MultiIndex
+from pandas import Index, Int64Index, MultiIndex
 import pandas._testing as tm
 
 
@@ -190,3 +190,35 @@ def test_pivot_list_like_columns(
         expected_values, columns=expected_columns, index=expected_index
     )
     tm.assert_frame_equal(result, expected)
+
+
+def test_pivot_multiindexed_rows_and_cols():
+    # GH 36360
+
+    df = pd.DataFrame(
+        data=np.arange(12).reshape(4, 3),
+        columns=MultiIndex.from_tuples(
+            [(0, 0), (0, 1), (0, 2)], names=["col_L0", "col_L1"]
+        ),
+        index=MultiIndex.from_tuples(
+            [(0, 0, 0), (0, 0, 1), (1, 1, 1), (1, 0, 0)],
+            names=["idx_L0", "idx_L1", "idx_L2"],
+        ),
+    )
+
+    res = df.pivot_table(
+        index=["idx_L0"],
+        columns=["idx_L1"],
+        values=[(0, 1)],
+        aggfunc=lambda col: col.values.sum(),
+    )
+
+    expected = pd.DataFrame(
+        data=[[5.0, np.nan], [10.0, 7.0]],
+        columns=MultiIndex.from_tuples(
+            [(0, 1, 0), (0, 1, 1)], names=["col_L0", "col_L1", "idx_L1"]
+        ),
+        index=Int64Index([0, 1], dtype="int64", name="idx_L0"),
+    )
+
+    tm.assert_frame_equal(res, expected)