Names are just a way to tie you to an identity, if you can rely on someone to always be under the same name you can treat it just as if it were their real name (even if it isn't). I run a large forum (a community) and a huge number of people have formed value relations through it and they exist under pseudonyms.
For me personally most people that know of me know me by my username (citricsquid) and wouldn't be able to tell you my real name, so if I appear on a website as "Samuel Ryan" they're not going to have a clue who I am and would gain a lot more value if I was displayed under the identity they know me as (citricsquid).
The reason Facebook uses real names is just because it's how people are known in real life, Facebook exists as an extension of real life and so using real names is the sensible decision that provides most value to users.
And even then, some people sign up to Facebook using a fake name, so that they can connect to some people they know in real life while avoiding other people they know in real life. (e.g. to talk to friends while avoiding colleagues and clients.)
That's not hard to imagine, people did it on MySpace and Friendster. These days, Facebook isn't really much better or different from those earlier social networks.