An alternative I am fond of is to to avoid introducing a new type, and simply initialize a PyObject * and register its address.  For example:

 PyObject *tmp;
 static PyObject *s_update;    // pick a naming convention

 PY_IDENTIFIER_INIT(update);
 tmp = PyObject_CallMethodObj(result, s_update, "O", other);

 (but also PyObject_GetAttr(o, s_update), etc.)

PY_IDENTIFIER_INIT(update) might expand to something like:

 if (!s_update) {
   s_update = PyUnicode_InternFromString("update");
   _Py_IdentifierAdd(&s_update);
 }