diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 5b5b0d70f6b2a..8bd62faacdcad 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -3974,7 +3974,7 @@ def asof(self, where, subset=None):
         nulls = self.isnull() if is_series else self[subset].isnull().any(1)
         if nulls.all():
             if is_series:
-                return pd.Series(np.nan, index=where)
+                return pd.Series(np.nan, index=where, name=self.name)
             else:
                 if is_list:
                     return pd.DataFrame(np.nan, index=where,
diff --git a/pandas/tests/series/test_asof.py b/pandas/tests/series/test_asof.py
index 4b9a2cf160910..ee6ab15b8963a 100644
--- a/pandas/tests/series/test_asof.py
+++ b/pandas/tests/series/test_asof.py
@@ -169,3 +169,7 @@ def test_all_nans(self):
         date = date_range('1/1/1990', periods=N * 3, freq='25s')[0]
         result = Series(np.nan, index=rng).asof(date)
         assert isnull(result)
+
+        # test name is propagated
+        result = Series(np.nan, index=[1, 2, 3, 4], name='test').asof([4, 5])
+        self.assertEqual(result.name, 'test')