Under your logic should identical twins self-identify as each other?

No? I guess I didn't make that clear enough but I was actually arguing against it when I further wrote, "It seems a lot, we stop caring about past reifications of our selfs...". At the end I conclude that the only time-consistent and reliable definition of identity can be based upon an agents utility function and therefore any agent that does not exhibit goal-stability will be prone to make inconsistent decisions.