Any name that a PC shinki remembers as "their name" can be used to return them from their vessel form. (In other words, if a "nickname" or alias is used for them in canon consistently enough that they arrive in game knowing that name, it'd count! If they're just given a nickname in-game, that would not be usable for any spells.)

It's also possible for just a given name, or just a surname, to be used, rather than having to call a character's full legal name to return them from vessel form.

That said, players should pick a consistent name for their character's god to use when calling them back, rather than switching it up -- after all, it is a spell, and varying spell words isn't recommended.