I've had a friend banned from facebook for using a nickname, instead of a real name. Facebook may not do it as often, or it may not be as publicized, but they do also have a real name policy in place.
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.
In light of how much money this policy is presumably making them, and considering that they have about a billion customers who seem to accept the policy as is, I strongly suspect they don't care in the least that the occasional person with an unusual name falls through the cracks, or that they're screwing over people who need to remain anonymous for legitimate safety reasons.
Do I agree with their decision? Not at all. But I think they know exactly what they're doing.
One point I want to clarify: I do think Facebook knows what they are doing in collecting marketing data, in the same way Bank of America knows what they are doing in holding bank accounts. What they are not doing well is creating an accurate representation of identity online. If you follow Chris Pool's thesis ("Identity is prismatic"), then nobody is doing this well right now.
On the minus side, some people on Facebook use reporting as a form of trolling, and it appears to be fairly easy to get people kicked off of Facebook with enough flagging persistence. For friends of mine who run a religious ministry, basically everything they post gets flagged, and they regularly get kicked off the site for a few days at a time. They've finally gotten it under control after several long phone conversations with FB support.