Sometime ago I got into hot water with Facebook and was banned due to the use of my name. Thankfully a developer at Facebook read my post and volunteered to look into the situtation for me. It would seem the problem they had with my original use of my name wasn't Barbie, but the fact that I used 'ThePerlMonger' as my surname because I didn't want my surname made public. I'm very grateful to the developer, as now I've had my account re-enabled.
However, that isn't quite the end, as although I originally said I was happy to provide them with my real name, I didn't want it made public. Thankfully the developer has acknowledged this and very kindly enabled the account without a surname. I think I'm currently the only person on Facebook to have a single name as their identity. So many thanks are due to the developer for taking an interest, when he really didn't need to. I owe him beer should I ever get to meet him :)
So if you get a friend request from 'Barbie' in the near future, it'll be me :)
There are *lots* of people with only one name, and I don't just mean weirdos like you and Abigail. Trying to shoe-horn names into particular formats and fields Just Doesn't Work. So these days, I just ask for:
And then I get over-ruled by Da Boss who thinks that asking for these things (with examples!) is too confusing for the users.