I can't get into my Facebook account right now because it's prompting me with a request to provide government-issued ID (eg, drivers license, passport) to verify me. Suffice it to say, I am no longer on Facebook.
FB might not be worth the trouble for you, but assuming someone really wanted to continue using it under a fake name, isn't this a viable option?
1. Created a fake account in one country and used it a few times, then many many months later I tried to login from another country and Facebook promptly required government-issued ID.
2. Created another fake account and changed the E-mail address after a few days and Facebook promptly required government-issued ID.
It makes me really happy that so many are deleting their Facebook account, or at least trying to use it less.