diff --git a/pytensor/graph/op.py b/pytensor/graph/op.py
index dd131cbdbc..160a65dd7a 100644
--- a/pytensor/graph/op.py
+++ b/pytensor/graph/op.py
@@ -246,7 +246,9 @@ def make_node(self, *inputs: Variable) -> Apply:
             )
         return Apply(self, inputs, [o() for o in self.otypes])
 
-    def __call__(self, *inputs: Any, **kwargs) -> Variable | list[Variable]:
+    def __call__(
+        self, *inputs: Any, name=None, return_list=False, **kwargs
+    ) -> Variable | list[Variable]:
         r"""Construct an `Apply` node using :meth:`Op.make_node` and return its outputs.
 
         This method is just a wrapper around :meth:`Op.make_node`.
@@ -288,8 +290,15 @@ def __call__(self, *inputs: Any, **kwargs) -> Variable | list[Variable]:
             the :attr:`Op.default_output` property.
 
         """
-        return_list = kwargs.pop("return_list", False)
         node = self.make_node(*inputs, **kwargs)
+        if name is not None:
+            if len(node.outputs) == 1:
+                node.outputs[0].name = name
+            elif self.default_output is not None:
+                node.outputs[self.default_output].name = name
+            else:
+                for i, n in enumerate(node.outputs):
+                    n.name = f"{name}_{i}"
 
         if config.compute_test_value != "off":
             compute_test_value(node)
diff --git a/tests/graph/test_op.py b/tests/graph/test_op.py
index 59d81ad59e..73f612c2f5 100644
--- a/tests/graph/test_op.py
+++ b/tests/graph/test_op.py
@@ -232,3 +232,46 @@ def perform(self, *_):
 
     x = pt.TensorType(dtype="float64", shape=(1,))("x")
     assert SomeOp()(x).type == pt.dvector
+
+
+@pytest.mark.parametrize("multi_output", [True, False])
+def test_call_name(multi_output):
+    def dummy_variable(name):
+        return Variable(MyType(thingy=None), None, None, name=name)
+
+    x = dummy_variable("x")
+
+    class TestCallOp(Op):
+        def __init__(self, default_output, multi_output):
+            super().__init__()
+            self.default_output = default_output
+            self.multi_output = multi_output
+
+        def make_node(self, input):
+            inputs = [input]
+            if self.multi_output:
+                outputs = [input.type(), input.type()]
+            else:
+                outputs = [input.type()]
+            return Apply(self, inputs, outputs)
+
+        def perform(self, node, inputs, outputs):
+            raise NotImplementedError()
+
+    if multi_output:
+        multi_op = TestCallOp(default_output=None, multi_output=multi_output)
+        res = multi_op(x, name="test_name")
+        for i, r in enumerate(res):
+            assert r.name == f"test_name_{i}"
+
+        multi_op = TestCallOp(default_output=1, multi_output=multi_output)
+        result = multi_op(x, name="test_name")
+        assert result.owner.outputs[0].name is None
+        assert result.name == "test_name"
+    else:
+        single_op = TestCallOp(default_output=None, multi_output=multi_output)
+        res_single = single_op(x, name="test_name")
+        assert res_single.name == "test_name"
+
+        res_nameless = single_op(x)
+        assert res_nameless.name is None