Take them to court over what exactly? Where's the damages? FB would have to show that being misinformed about your name cost them anything whatsoever. They could try getting the DA to prosecute you under computer fraud and abuse (unauthorized access to a computer system under a false identity). Even that is a huge risk. Imagine the precedent set if the jury decides to nullify, and what sane jury wouldn't nullify over the charge of "set up a fb account under a fake name and ID"? And does the DA really want to risk gaining a reputation for being FB lapdog?

The truth is, FB demands an ID but they have no real right or basis for making this demand.