Shit!
Can't you ask for alternative ways to verify?
In my opinion, even if you have a fake name, you can provide your ID document. Just say that you didn't want to use your real name.
If you are a man, and your profile is a woman, then ask a girl friend to show up as you; again, if the name is not the same, it is okay.
Do you have also a fake picture on your profile?
I would like to know what's up with your case, I work a lot there right now haha