The important point, PB, is indicated in China Doll's post.
Facebook expects to provide a name and a picture. Theoretically that's your real name and your real face but there's nothing to prevent anyone from using a false name (such as their AB username) and a fake picture (such as one of Marilyn Monroe, Jessica Rabbit or anything else). Further, just as on AB, people can sign up with multiple identities. (So a user can have a 'real' Facebook page and lots of 'fake' ones as well).