"Lil Miss Hot Mess" is a stage name, and I am not obligated to recognize it. I actually find it not comparable at all to compare it to someone's gender-identified pronouns and perfectly applicable to what OP was saying.
In other words, because you don't like the name "Lil Miss Hot Mess" (I assume because it is not as serious as "Joe" or "Torgo", as names go), is it OK to call anyone by whatever name you prefer, and refuse to acknowledge them as anything else? Whether I think "Lil Miss Hot Mess" is a ridiculous name or not doesn't alter the reality that facebook daily "disappears" people's accounts whose names aren't up to their standards. This change in policy gives people a week to protest that disappearance, but it doesn't change facebook's level of control. They still decide who you can be online (at least on facebook).
The thing is that I don't know where to draw that line on what is "too ridiculous", and I don't think anyone else really does, either. So, given that names are arbitrary (even when enforcing a "real names" policy, there are people who have ridiculous names), and given that enforcing a real names policy harms countless people, and given that not enforcing real names has very little negative result except to facebook's bottom line (and even that is negligible), I just don't see it as defensible.
The argument that it prevents abuse and bullying is shown to be a lie by the fact that this policy has been used, since facebook's inception, to bully people, and facebook has for all that time remained complicit, and even an active participant, in that bullying. You can't claim to want to prevent bullying if you're the one holding the victim down while someone else punches them.
No one can make you call Lil Miss Hot Mess by her chosen name, but, ethically, I don't think anyone can tell her not to go by that name, and I don't believe it is ethical to demand she "prove" that's the name she wants to go by, either. If she says it's the name she prefers...well, who would know better what she wants?
FB: "Our policy has never been to require everyone on Facebook to use their legal name. The spirit of our policy is that everyone on Facebook uses the authentic name they use in real life. For Sister Roma, that's Sister Roma. For Lil Miss Hot Mess, that's Lil Miss Hot Mess."
Not using someone's preferred name / gender pronouns is plain and simple being an asshole. Nobody really gives a shit about your opinions on being trans or whatever -- we've literally heard every argument you could possibly make many, many times. Just don't be an asshole so my day isn't ruined and I can pretend your outdated views don't exist.