@ERode, well, when you first come into contact with your spirit they (usually) state their name, and even if they don't, the Connector can find out by seeing the relations between his powers and myths. And their identities are confirmed after you start using their powers (At least in the case of famous spirits), because, well, even if a spirit claimed that it was King Arthur and couldn't bring out Excalibur, that'd be fishy, don't ya think? :P
Basically, by the usage of powers is how they confirm who or what their spirits are.
@shadowkiller, good to know, I hope that over the course of those days we don't do much, maybe next plot post and that's a maybe.