Kaz,
When you login with JFBConnect, it should fetch their email and first/last name to populate the "Name" field. Those are the required fields of Joomla, and JFBConnect will always fetch and use them when registering.
To get more information, you can use our Social Profile plugins to import extra data into a user's profile in Community Builder, JomSocial, Kunena or multiple other systems we support.
I hope that answers your questions, but if there was something more specific you were looking for, just let us know.
Thanks,
Alex