BUG: name attr in RangeIndex.intersection

pandas/conftest.py

@@ -1432,3 +1432,17 @@ def __init__(self, **kwargs):
     registry.pop("testmem", None)
     TestMemoryFS.test[0] = None
     TestMemoryFS.store.clear()
+
+
+@pytest.fixture(
+    params=[
+        ("foo", None, None),
+        ("Egon", "Venkman", None),
+        ("NCC1701D", "NCC1701D", "NCC1701D"),
+    ]
+)
+def names(request):
+    """
+    A 3-tuple of names, the first two for operands, the last for a result.
+    """
+    return request.param

pandas/core/indexes/range.py

@@ -15,6 +15,7 @@
 from pandas.core.dtypes.common import (
     ensure_platform_int,
     ensure_python_int,
+    is_dtype_equal,
     is_float,
     is_integer,
     is_list_like,
@@ -504,13 +505,26 @@ def intersection(self, other, sort=False):
         intersection : Index
         """
         self._validate_sort_keyword(sort)
+        self._assert_can_do_setop(other)
+        other, _ = self._convert_can_do_setop(other)
 
-        if self.equals(other):
+        if self.equals(other) and not self.has_duplicates:
+            # has_duplicates check is unnecessary for RangeIndex, but
+            #  used to match other subclasses.
             return self._get_reconciled_name_object(other)
 
-        if not isinstance(other, RangeIndex):
+        if not is_dtype_equal(self.dtype, other.dtype):
             return super().intersection(other, sort=sort)
 
+        result = self._intersection(other, sort=sort)
+        return self._wrap_setop_result(other, result)
+
+    def _intersection(self, other, sort=False):
+
+        if not isinstance(other, RangeIndex):
+            # Int64Index
+            return super()._intersection(other, sort=sort)
+
         if not len(self) or not len(other):
             return self._simple_new(_empty_range)
 
@@ -551,7 +565,7 @@ def intersection(self, other, sort=False):
         if sort is None:
             new_index = new_index.sort_values()
 
-        return self._wrap_setop_result(other, new_index)
+        return new_index
 
     def _min_fitting_element(self, lower_limit: int) -> int:
         """Returns the smallest element greater than or equal to the limit"""

pandas/tests/arithmetic/conftest.py

@@ -18,18 +18,6 @@ def id_func(x):
 
 
 # ------------------------------------------------------------------
-@pytest.fixture(
-    params=[
-        ("foo", None, None),
-        ("Egon", "Venkman", None),
-        ("NCC1701D", "NCC1701D", "NCC1701D"),
-    ]
-)
-def names(request):
-    """
-    A 3-tuple of names, the first two for operands, the last for a result.
-    """
-    return request.param
 
 
 @pytest.fixture(params=[1, np.array(1, dtype=np.int64)])

pandas/tests/indexes/ranges/test_setops.py

@@ -37,6 +37,18 @@ def test_intersection_mismatched_dtype(self, klass):
         result = flt[:0].intersection(index)
         tm.assert_index_equal(result, flt[:0], exact=True)
 
+    def test_intersection_empty(self, sort, names):
+        # name retention on empty intersections
+        index = RangeIndex(start=0, stop=20, step=2, name=names[0])
+
+        # empty other
+        result = index.intersection(index[:0].rename(names[1]), sort=sort)
+        tm.assert_index_equal(result, index[:0].rename(names[2]), exact=True)
+
+        # empty self
+        result = index[:0].intersection(index.rename(names[1]), sort=sort)
+        tm.assert_index_equal(result, index[:0].rename(names[2]), exact=True)
+
     def test_intersection(self, sort):
         # intersect with Int64Index
         index = RangeIndex(start=0, stop=20, step=2)
@@ -78,12 +90,12 @@ def test_intersection(self, sort):
         result = other.intersection(first, sort=sort).astype(int)
         tm.assert_index_equal(result, expected)
 
-        index = RangeIndex(5)
+        index = RangeIndex(5, name="foo")
 
         # intersect of non-overlapping indices
-        other = RangeIndex(5, 10, 1)
+        other = RangeIndex(5, 10, 1, name="foo")
         result = index.intersection(other, sort=sort)
-        expected = RangeIndex(0, 0, 1)
+        expected = RangeIndex(0, 0, 1, name="foo")
         tm.assert_index_equal(result, expected)
 
         other = RangeIndex(-1, -5, -1)
@@ -100,11 +112,12 @@ def test_intersection(self, sort):
         result = other.intersection(index, sort=sort)
         tm.assert_index_equal(result, expected)
 
+    def test_intersection_non_overlapping_gcd(self, sort, names):
         # intersection of non-overlapping values based on start value and gcd
-        index = RangeIndex(1, 10, 2)
-        other = RangeIndex(0, 10, 4)
+        index = RangeIndex(1, 10, 2, name=names[0])
+        other = RangeIndex(0, 10, 4, name=names[1])
         result = index.intersection(other, sort=sort)
-        expected = RangeIndex(0, 0, 1)
+        expected = RangeIndex(0, 0, 1, name=names[2])
         tm.assert_index_equal(result, expected)
 
     def test_union_noncomparable(self, sort):