Note that I said privacy, not anonymity. It's privacy in the sense that it really does prevent Facebook and governments from tracing from which location you're logging in. It isn't anonymity because you're expected to go by your real name on Facebook (by peers), and they automatically disable fake sounding names. (Although you can still use a fake name that sounds real, and give your peers the impression that that's your real name. If, for some reason, you want to do that.)