Regression in loc.setitem losing mi names when df is empty

doc/source/whatsnew/v1.4.2.rst

@@ -17,6 +17,7 @@ Fixed regressions
 - Fixed regression in :meth:`DataFrame.drop` and :meth:`Series.drop` when :class:`Index` had extension dtype and duplicates (:issue:`45860`)
 - Fixed memory performance regression in :meth:`Series.fillna` when called on a :class:`DataFrame` column with ``inplace=True`` (:issue:`46149`)
 - Provided an alternative solution for passing custom Excel formats in :meth:`.Styler.to_excel`, which was a regression based on stricter CSS validation. Examples available in the documentation for :meth:`.Styler.format` (:issue:`46152`)
+- Fixed regression in :meth:`DataFrame.loc.__setitem__` losing :class:`MultiIndex` names if :class:`DataFrame`  was empty before (:issue:`46317`)
 -
 
 .. ---------------------------------------------------------------------------

pandas/core/indexing.py

@@ -2094,7 +2094,14 @@ def _setitem_with_indexer_missing(self, indexer, value):
                 # We will ignore the existing dtypes instead of using
                 #  internals.concat logic
                 df = value.to_frame().T
-                df.index = Index([indexer], name=self.obj.index.name)
+
+                idx = self.obj.index
+                if isinstance(idx, MultiIndex):
+                    name = idx.names
+                else:
+                    name = idx.name
+
+                df.index = Index([indexer], name=name)
                 if not has_dtype:
                     # i.e. if we already had a Series or ndarray, keep that
                     #  dtype.  But if we had a list or dict, then do inference

pandas/tests/frame/indexing/test_indexing.py

@@ -1281,6 +1281,18 @@ def test_loc_expand_empty_frame_keep_index_name(self):
         expected = DataFrame({"b": [1]}, index=Index([0], name="a"))
         tm.assert_frame_equal(df, expected)
 
+    def test_loc_expand_empty_frame_keep_midx_names(self):
+        # GH#46317
+        df = DataFrame(
+            columns=["d"], index=MultiIndex.from_tuples([], names=["a", "b", "c"])
+        )
+        df.loc[(1, 2, 3)] = "foo"
+        expected = DataFrame(
+            {"d": ["foo"]},
+            index=MultiIndex.from_tuples([(1, 2, 3)], names=["a", "b", "c"]),
+        )
+        tm.assert_frame_equal(df, expected)
+
 
 class TestDataFrameIndexingUInt64:
     def test_setitem(self, uint64_frame):