There's no way to do what you're looking for. The Facebook Comments widget is provided from Facebook. Any user visiting your site, that's logged into Facebook.com, can create a post there. It's not necessary for them to actually have an account on your site.
Facebook will also not let you permanently delete comments from users. You can 'hide' them, but those comments will still be visible to the original poster and that poster's friends. That's likely not a large group though, so hiding does effectively remove the comment from your site. Banning the user from commenting again will also prevent future comments from that user.
As for moderation in general, you can obviously do that on each post where the comment box is displayed. You can also see a list of all comments for your site on the page below:
developers.facebook.com/tools/comments
That may help you search for a specific user name to remove/hide any comments from your site.
Finally, JFBConnect can be configured to notify you of all new FB comments in the Social -> Notifications area. That at least helps keep up to speed with any new comments being posted on your site.
I hope that helps, but if not, or you have other questions, just let me know!
Thanks,
Alex
Auto-remove facebook comments for deleted/suspended users.
