In Mystery Dungeon the protagonist is a human turned into a Pokemon which decided through randomized personality quiz and the gender you pick and you decide the name as well as the partner Pokemon. Both the protagonist and the partner have a set and defined character and dialogue/inner monologue that's not affected by which Pokemon or the quiz result though, and the few times you can decide an answer to give have no effect on development or the partner's overall relationship with the protagonist.

So it's literally a set personality and background with no set physical identity attached to it.

I dunno if I'm making it clear enough, and I don't know of any other potential examples to liken it to sadly.