Sort of. If they have reason to suspect that you're not using your real name, then they'll ask for ID, and they may shut down your account.
I'm not surprised that you wouldn't know, though, since trans people are among the only ones who are actually affected by that policy on a regular basis. A cis person can change their name to whatever they want without issue, usually; however, Facebook follows up on reports when a lot of people report a single thing, so if a hundred people report a trans person's name as "not their real name" because they want to be transphobic pieces of shit, then Facebook will ask for ID.
There are a lot of unsavoury things that Facebook does, actually, but I still use it because it's the foundation for most of my social network. I'd lose touch with most of my friends without it.