diff --git a/src/openai/lib/streaming/responses/_responses.py b/src/openai/lib/streaming/responses/_responses.py
index 6975a9260d..39b44a1239 100644
--- a/src/openai/lib/streaming/responses/_responses.py
+++ b/src/openai/lib/streaming/responses/_responses.py
@@ -304,6 +304,14 @@ def handle_event(self, event: RawResponseStreamEvent) -> List[ResponseStreamEven
                     snapshot=output.arguments,
                 )
             )
+        elif event.type == "response.function_call_arguments.done":
+            output = snapshot.output[event.output_index]
+            assert output.type == "function_call"
+
+            if not event.name:
+                event.name = output.name
+
+            events.append(event)
 
         elif event.type == "response.completed":
             response = self._completed_response
diff --git a/tests/lib/responses/test_function_call_done_event.py b/tests/lib/responses/test_function_call_done_event.py
new file mode 100644
index 0000000000..eaadb4f562
--- /dev/null
+++ b/tests/lib/responses/test_function_call_done_event.py
@@ -0,0 +1,117 @@
+from __future__ import annotations
+
+from openai._types import omit
+from openai._models import construct_type_unchecked
+from openai.types.responses import ResponseStreamEvent as RawResponseStreamEvent
+from openai.lib.streaming.responses._responses import ResponseStreamState
+
+
+def _event(value: dict[str, object]) -> RawResponseStreamEvent:
+    return construct_type_unchecked(type_=RawResponseStreamEvent, value=value)
+
+
+def test_function_call_done_name_falls_back_to_snapshot() -> None:
+    state = ResponseStreamState(text_format=omit, input_tools=omit)
+
+    state.handle_event(
+        _event(
+            {
+                "type": "response.created",
+                "sequence_number": 0,
+                "response": {
+                    "id": "resp_123",
+                    "object": "response",
+                    "created_at": 0,
+                    "status": "in_progress",
+                    "output": [],
+                },
+            }
+        )
+    )
+    state.handle_event(
+        _event(
+            {
+                "type": "response.output_item.added",
+                "sequence_number": 1,
+                "output_index": 0,
+                "item": {
+                    "id": "fc_123",
+                    "type": "function_call",
+                    "call_id": "call_123",
+                    "name": "search_parts",
+                    "arguments": "{}",
+                    "status": "in_progress",
+                },
+            }
+        )
+    )
+
+    events = state.handle_event(
+        _event(
+            {
+                "type": "response.function_call_arguments.done",
+                "sequence_number": 2,
+                "item_id": "fc_123",
+                "output_index": 0,
+                "arguments": "{}",
+                "name": None,
+            }
+        )
+    )
+
+    assert len(events) == 1
+    event = events[0]
+    assert event.type == "response.function_call_arguments.done"
+    assert event.name == "search_parts"
+
+
+def test_function_call_done_preserves_server_name() -> None:
+    state = ResponseStreamState(text_format=omit, input_tools=omit)
+
+    state.handle_event(
+        _event(
+            {
+                "type": "response.created",
+                "sequence_number": 0,
+                "response": {
+                    "id": "resp_123",
+                    "object": "response",
+                    "created_at": 0,
+                    "status": "in_progress",
+                    "output": [],
+                },
+            }
+        )
+    )
+    state.handle_event(
+        _event(
+            {
+                "type": "response.output_item.added",
+                "sequence_number": 1,
+                "output_index": 0,
+                "item": {
+                    "id": "fc_123",
+                    "type": "function_call",
+                    "call_id": "call_123",
+                    "name": "search_parts",
+                    "arguments": "{}",
+                    "status": "in_progress",
+                },
+            }
+        )
+    )
+
+    events = state.handle_event(
+        _event(
+            {
+                "type": "response.function_call_arguments.done",
+                "sequence_number": 2,
+                "item_id": "fc_123",
+                "output_index": 0,
+                "arguments": "{}",
+                "name": "server_name",
+            }
+        )
+    )
+
+    assert events[0].name == "server_name"