diff --git a/instructor/v2/dsl/iterable.py b/instructor/v2/dsl/iterable.py
index c47e92b09..5a0f3bb35 100644
--- a/instructor/v2/dsl/iterable.py
+++ b/instructor/v2/dsl/iterable.py
@@ -267,13 +267,15 @@ def from_streaming_response(cls, completion) -> Generator[User]:
         task_name = name
     else:
         # Handle `Union[A, B]` / `A | B` task types.
-        # `types.UnionType` does not have `__name__`, so fall back to a stable name.
-        task_name = getattr(subtask_class, "__name__", None)
-        if task_name is None and get_origin(subtask_class) in _UNION_ORIGINS:
+        # Both `typing.Union[A, B]` and PEP 604 `A | B` expose ``__name__ == "Union"``
+        # (and `types.UnionType` normalizes to ``typing.Union`` on modern Python), so we
+        # must detect a union *origin* first and build the name from its members --
+        # otherwise every union collapses to the unhelpful ``IterableUnion``.
+        if get_origin(subtask_class) in _UNION_ORIGINS:
             members = get_args(subtask_class)
             task_name = "Or".join(getattr(m, "__name__", str(m)) for m in members)
-        if task_name is None:
-            task_name = str(subtask_class)
+        else:
+            task_name = getattr(subtask_class, "__name__", None) or str(subtask_class)
 
     name = f"Iterable{task_name}"
 
diff --git a/tests/dsl/test_simple_types.py b/tests/dsl/test_simple_types.py
index 9e9aca9f3..3202a4099 100644
--- a/tests/dsl/test_simple_types.py
+++ b/tests/dsl/test_simple_types.py
@@ -170,3 +170,43 @@ class B(BaseModel):
     assert "|" not in prepared.__name__
     assert "." not in prepared.__name__
     assert prepared.__name__ == "IterableAOrB"
+
+
+def test_list_of_model_typing_union_generates_clean_name():
+    """`List[Union[A, B]]` must derive its Iterable name from the union members.
+
+    Both `typing.Union[A, B]` and PEP 604 `A | B` expose ``__name__ == "Union"``, so a
+    naive ``__name__`` lookup collapses every union to ``IterableUnion``. The name should
+    instead be built from the member names (``IterableAOrB``).
+    """
+
+    class A(BaseModel):
+        x: int
+
+    class B(BaseModel):
+        y: str
+
+    prepared = prepare_response_model(List[Union[A, B]])  # noqa: UP006
+    assert prepared is not None
+    assert prepared.__name__ == "IterableAOrB"
+
+
+@pytest.mark.skipif(
+    sys.version_info < (3, 10),
+    reason="Union pipe syntax is only available in Python 3.10+",
+)
+def test_list_of_model_three_way_union_generates_clean_name():
+    """A union with more than two members joins every member name with ``Or``."""
+
+    class A(BaseModel):
+        x: int
+
+    class B(BaseModel):
+        y: str
+
+    class C(BaseModel):
+        z: float
+
+    prepared = prepare_response_model(list[A | B | C])
+    assert prepared is not None
+    assert prepared.__name__ == "IterableAOrBOrC"