Peter,
Right now, JFBConnect will use the 'Full Name' value that Facebook returns. This is set by the user in Facebook as the "Display as:" setting in their Account Settings area. So, whats being used in Joomla is what the user has chosen to show as their name in Facebook, and what I'd recommend using on your site, if the name is visible to others.
With that said, with just a little bit of code, we could easily help you modify our default behavior to always include the middle name, if that's what you'd prefer.
Thanks,
Alex