diff --git a/doc/source/whatsnew/v1.1.2.rst b/doc/source/whatsnew/v1.1.2.rst
index da261907565a1..c40430256f64b 100644
--- a/doc/source/whatsnew/v1.1.2.rst
+++ b/doc/source/whatsnew/v1.1.2.rst
@@ -42,6 +42,7 @@ Bug fixes
 - 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 in :meth:`DataFrame.corr` causing subsequent indexing lookups to be incorrect (:issue:`35882`)
 - Bug in :meth:`import_optional_dependency` returning incorrect package names in cases where package name is different from import name (:issue:`35948`)
+- Bug when setting empty :class:`DataFrame` column to a :class:`Series` in preserving name of index in frame (:issue:`31368`)
 
 .. ---------------------------------------------------------------------------
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index e1a889bf79d95..59cf4c0e2f81d 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..7afbbc2b9ab2b 100644
--- a/pandas/tests/indexing/test_partial.py
+++ b/pandas/tests/indexing/test_partial.py
@@ -660,3 +660,15 @@ 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
+        expected = pd.DataFrame(
+            {"series": [1.23] * 4}, index=pd.RangeIndex(4, name="df_index")
+        )
+
+        tm.assert_frame_equal(df, expected)