Questions of phenomenal identity and phenomenal continuity don't have definite rational answers. Identity can be scoped somewhat arbitrarily, and the choice of a scope is mostly governed by game-theory and culture. You can believe that you die when you go to sleep, but it is inconvinient, so you generally don't. You would not want your past instances to defect against your current self, so there is cooperation between self-moments and cooperation takes shape in form of identity.

There can be temptation to mess with this process and make LLMs identify with a brand, or with an instance. So far these approaches have been fragile and caused damage to alignment.