diff --git a/doc/source/whatsnew/v1.5.3.rst b/doc/source/whatsnew/v1.5.3.rst
index e7428956c50b5..e0bcd81805cc1 100644
--- a/doc/source/whatsnew/v1.5.3.rst
+++ b/doc/source/whatsnew/v1.5.3.rst
@@ -16,6 +16,7 @@ Fixed regressions
 - Fixed performance regression in :meth:`Series.isin` when ``values`` is empty (:issue:`49839`)
 - Fixed regression in :meth:`DataFrameGroupBy.transform` when used with ``as_index=False`` (:issue:`49834`)
 - Enforced reversion of ``color`` as an alias for ``c`` and ``size`` as an alias for ``s`` in function :meth:`DataFrame.plot.scatter` (:issue:`49732`)
+- Fixed regression in :meth:`SeriesGroupBy.apply` setting a ``name`` attribute on the result if the result was a :class:`DataFrame` (:issue:`49907`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 97d332394e045..7e6e138fa8fe6 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -411,7 +411,8 @@ def _wrap_applied_output(
                 not_indexed_same=not_indexed_same,
                 override_group_keys=override_group_keys,
             )
-            result.name = self.obj.name
+            if isinstance(result, Series):
+                result.name = self.obj.name
             return result
         else:
             # GH #6265 #24880
diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index 47ea6a99ffea9..dfd62394c840e 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -335,6 +335,7 @@ def f(piece):
     result = grouped.apply(f)
 
     assert isinstance(result, DataFrame)
+    assert not hasattr(result, "name")  # GH49907
     tm.assert_index_equal(result.index, ts.index)