Facebook is not anonymous. That is enforced and by design, and fairly important in distinguishing it from other social networks. The rest of your points are still fair though.
I'm an over-fifty user of Facebook, and I've noticed that a lot of my friends (some over fifty, and some not) have figured out how to fake their names in various ways. Among my friends, it is more often women than men who go by fake names, for the usual Internet security concerns that women have about cyberstalkers.
It's all totally fake info that I use to play scrabble with my dentist, who also has a completely fake account.