There's a few options for you:
* With Automatic Registration, set the prefix in JFBConnect to something like firlas or first.last instead of fb_, g_. They still won't be able to change their username, but it will be a prettier one, at least.
* Switch to "Normal Registration" in JFBConnect. That will present the user with a registration form when they sign in. You can disable the email and password fields on that form though, so all it would show is a username field. You can even have JFBConnect/JLinked pre-fill a username (using the prefix setting) so the user doesn't have to do much thinking unless they want to.
Finally, Joomla doesn't let user's change their username's by default. I believe there are some plugins for Joomla that will enable that ability though. However, there are some extensions that also choke if a user does change their username since their database tables use the username as a looking instead of the user ID (which is what should be used, since that never changes).
I hope that helps explain, but if you have any other questions or feedback, just let me know.
Thanks,
Alex