You raise an interesting point about having a 'fake' name to show the world, and what is your real name.
I'm Chinese, so on my bank accounts and official documents, I have the romanised version of my name in mandarin.
In day to day life however, everyone calls me Nicholas. My co workers, clients, friends, etc. and that is also the name I use on facebook. About the only people who know my name in mandarin are my immediate family, and entities I need to enter into contracts with.
To be sure, Nicholas is by no means fake or a pseudonym. My parents named me as such, and I have answered to that name all my life. Google me and you will turn up a lot of stuff i have put online over the years, pictures of parties, videos, random nonsense on forums etc. But searching official records for that name is going to turn up a lot of people who arn't me.
So back to the topic at hand, maybe what facebook is concerned with are name that are pure fiction/fantasy, after all, my name would pass the 'fake' test in the article as i have built an identity around it, but it's not my official name.