I think the lesson here is not to be too much attached to words.
They are important only inasmuch as they "pay rent", that is, they describe a useful distinction in the real world. Once it's seen that "identity" is a fluid concept, there's no point in trying to distinguish where exactly its boundaries are in the space of possible ideas. You just accept that the concept does not live up very well to reality, and it's your duty to update your mental model.
(BTW, I'm playing Talos these days and I find it cute...)