Identity is as much a social structure as a personal one. E.g. in star trek, when Will riker is duplicated. Both have continuity of memory, but Thomas has his continuity of identity broken. Though he doesn’t realise this until he meets his eigen twin, who’s been continuing on. Even though both are nominally identical at the moment of creation, Will’s continuation of his career maintained continuity of identity. Thomas Riker had his broken by being stranded. Hence why Thomas changed his name, while Will continued using Will.