From 9b6634e7b91452a28029bd8657461e13b3b6fefe Mon Sep 17 00:00:00 2001
From: Irv Lustig <irv@princeton.com>
Date: Sat, 5 Sep 2020 10:53:39 -0400
Subject: [PATCH 1/2] BUG: retain index name when dataframe has zero length,
 assiging a series

---
 pandas/core/frame.py                  | 8 +++++---
 pandas/tests/indexing/test_partial.py | 9 +++++++++
 2 files changed, 14 insertions(+), 3 deletions(-)

diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index c48bec9b670ad..95aed996dddd9 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -3206,9 +3206,11 @@ def _ensure_valid_index(self, value):
                     "and a value that cannot be converted to a Series"
                 ) from err
 
-            self._mgr = self._mgr.reindex_axis(
-                value.index.copy(), axis=1, fill_value=np.nan
-            )
+            # GH31368 preserve name of index
+            index_copy = value.index.copy()
+            index_copy.name = self.index.name
+
+            self._mgr = self._mgr.reindex_axis(index_copy, axis=1, fill_value=np.nan)
 
     def _box_col_values(self, values, loc: int) -> Series:
         """
diff --git a/pandas/tests/indexing/test_partial.py b/pandas/tests/indexing/test_partial.py
index 350f86b4e9fd0..12d759b8937ec 100644
--- a/pandas/tests/indexing/test_partial.py
+++ b/pandas/tests/indexing/test_partial.py
@@ -660,3 +660,12 @@ def test_indexing_timeseries_regression(self):
         expected = Series(rng, index=rng)
 
         tm.assert_series_equal(result, expected)
+
+    def test_index_name_empty(self):
+        # GH 31368
+        df = pd.DataFrame({}, index=pd.RangeIndex(0, name="df_index"))
+        series = pd.Series(1.23, index=pd.RangeIndex(4, name="series_index"))
+
+        df["series"] = series
+
+        tm.assert_equal(df.index.name, "df_index")

From 77d9c9e14e555dc94d043bae79c09e14e2074e0a Mon Sep 17 00:00:00 2001
From: Irv Lustig <irv@princeton.com>
Date: Sat, 5 Sep 2020 10:57:04 -0400
Subject: [PATCH 2/2] add whatsnew

---
 doc/source/whatsnew/v1.1.2.rst | 1 +
 1 file changed, 1 insertion(+)

diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index d1a66256454ca..2343ab2cb2c61 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -36,6 +36,7 @@ Bug fixes
 - Bug in :meth:`Float64Index.__contains__` incorrectly raising ``TypeError`` instead of returning ``False`` (:issue:`35788`)
 - Bug in :meth:`Series.dt.isocalendar` and :meth:`DatetimeIndex.isocalendar` that returned incorrect year for certain dates (:issue:`36032`)
 - Bug in :class:`DataFrame` indexing returning an incorrect :class:`Series` in some cases when the series has been altered and a cache not invalidated (:issue:`33675`)
+- Bug when setting empty :class:`DataFrame` column to a :class:`Series` in preserving name of index in frame (:issue:`31368`)
 
 .. ---------------------------------------------------------------------------