diff --git a/src/agents/run.py b/src/agents/run.py
index 66d3d9da..ee8125dd 100644
--- a/src/agents/run.py
+++ b/src/agents/run.py
@@ -1972,6 +1972,7 @@ class AgentRunner:
                 conversation_id=conversation_id,
                 session=session,
                 run_state=run_state,
+                trace_workflow_name=trace_workflow_name,
                 is_resumed_state=is_resumed_state,
                 sandbox_runtime=sandbox_runtime,
             )
diff --git a/src/agents/run_internal/run_loop.py b/src/agents/run_internal/run_loop.py
index e1e1bd84..65d4e794 100644
--- a/src/agents/run_internal/run_loop.py
+++ b/src/agents/run_internal/run_loop.py
@@ -606,6 +606,7 @@ async def start_streaming(
     session: Session | None,
     run_state: RunState[TContext] | None = None,
     *,
+    trace_workflow_name: str,
     is_resumed_state: bool = False,
     sandbox_runtime: SandboxRuntime[TContext] | None = None,
 ):
@@ -628,10 +629,9 @@ async def start_streaming(
             auto_previous_response_id=auto_previous_response_id,
         )
 
-    current_trace = streamed_result.trace or get_current_trace()
     use_task_and_turn_spans = include_task_and_turn_spans(run_config.tracing)
     current_task_span: Span[TaskSpanData] | None = (
-        task_span(name=current_trace.name) if current_trace and use_task_and_turn_spans else None
+        task_span(name=trace_workflow_name) if use_task_and_turn_spans else None
     )
     if current_task_span:
         current_task_span.start(mark_as_current=True)
diff --git a/tests/test_agent_tracing.py b/tests/test_agent_tracing.py
index c60477cf..2a629926 100644
--- a/tests/test_agent_tracing.py
+++ b/tests/test_agent_tracing.py
@@ -992,6 +992,31 @@ async def test_wrapped_streaming_run_creates_root_task_span():
     assert generation_spans[0].parent_id == turn_spans[0]["id"]
 
 
+@pytest.mark.asyncio
+async def test_wrapped_run_task_span_uses_run_workflow_name():
+    def _make_agent() -> Agent[None]:
+        return Agent(
+            name="test_agent",
+            model=FakeModel(initial_output=[get_text_message("first_test")]),
+        )
+
+    run_config = RunConfig(workflow_name="inner_workflow")
+
+    with trace(workflow_name="outer_workflow"):
+        await Runner.run(_make_agent(), input="first_test", run_config=run_config)
+        result = Runner.run_streamed(_make_agent(), input="first_test", run_config=run_config)
+        async for _ in result.stream_events():
+            pass
+
+    task_spans = [span.export() for span in fetch_ordered_spans() if span.span_data.type == "task"]
+    # A task span names one Runner invocation, so both runs must use their own workflow name
+    # rather than the enclosing trace's name.
+    assert [span["span_data"]["data"]["name"] for span in task_spans if span] == [
+        "inner_workflow",
+        "inner_workflow",
+    ]
+
+
 @pytest.mark.asyncio
 async def test_wrapped_streaming_run_can_disable_task_and_turn_spans():
     agent = Agent(