This is true! I don't think it does any harm not to rush into it. A name can be a very important thing.

[It's how they identify themselves, after all. There still remains the idea, however, that all of their familiars already have names and simply haven't chosen to share them. She can't discount that as a possibility.]

Either way, I don't think I'm lacking for options now. It'll just have to pick the one that it likes most.