For newer Facebook users (users who have created accounts in the last 60 days or so - it's hard to get an exact timeframe), the login panel won't show their name or profile picture. Also, the user information in the WP-Admin system doesn't have their name either. Their name does show down by the comment box by a post though.
I've setup myself a test facebook account to try to troubleshoot this and been through every privacy setting I can think of. Using other facebook connect sites worked just fine with the account - just not a wordpress site. I've tried to trouble shoot the code, but had little success.
I've tried different versions of the WP-FacebookConnect plugin. I'm even currently using the development version. It hasn't seemed to make any difference.