Also, it's important to separate the notion of a "real name" from a legal (wallet) name. A legal name shows up on government issued ID, and is called "legal" because it falls within the law of that government.
A "real" name, to me, is a label that can refer to an individual, animal, place, or thing within a given context. For example, I consider "aestetix" just as real as any other name, and there are some people who have known me for over a decade, solely by "aestetix." To them, it's quite a real name.
But consider people who use different names for political reasons, social reasons, safety reasons, etc. Mark Twain, Voltaire, Richard Bachman (aka Stephen King), and so on all had very legitimate reasons for using a non legal name. Imagine you're trying to post updates on Facebook about awful things your oppressive country is doing to you (think Iran or Syria). Or imagine that you have a stalker who is trying to hunt you down. The list goes on.
I think it's pretty obvious that none of the major websites have thought this stuff out very well.