diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index 04b5fc505c074f..92d0e6de0dfb93 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -293,6 +293,8 @@ get_running_loop(asyncio_state *state, PyObject **loop)
             }
         }
 
+        // TODO GH-121621: This should be moved to PyThreadState
+        // for easier and quicker access.
         state->cached_running_loop = rl;
         state->cached_running_loop_tsid = ts_id;
     }
@@ -336,6 +338,9 @@ set_running_loop(asyncio_state *state, PyObject *loop)
         return -1;
     }
 
+
+    // TODO GH-121621: This should be moved to PyThreadState
+    // for easier and quicker access.
     state->cached_running_loop = loop; // borrowed, kept alive by ts_dict
     state->cached_running_loop_tsid = PyThreadState_GetID(tstate);
 
@@ -1616,6 +1621,7 @@ FutureIter_dealloc(futureiterobject *it)
         state = get_asyncio_state(module);
     }
 
+    // TODO GH-121621: This should be moved to thread state as well.
     if (state && state->fi_freelist_len < FI_FREELIST_MAXLEN) {
         state->fi_freelist_len++;
         it->future = (FutureObj*) state->fi_freelist;
@@ -2146,7 +2152,12 @@ _asyncio_Task___init___impl(TaskObj *self, PyObject *coro, PyObject *loop,
         // optimization: defer task name formatting
         // store the task counter as PyLong in the name
         // for deferred formatting in get_name
-        name = PyLong_FromUnsignedLongLong(++state->task_name_counter);
+#ifdef Py_GIL_DISABLED
+        unsigned long long counter = _Py_atomic_add_uint64(&state->task_name_counter, 1) + 1;
+#else
+        unsigned long long counter = ++state->task_name_counter;
+#endif
+        name = PyLong_FromUnsignedLongLong(counter);
     } else if (!PyUnicode_CheckExact(name)) {
         name = PyObject_Str(name);
     } else {