Those poor fools

trans people wielding immense power in the fae wilds

Not a DND expert but generally the trope with Fey is that their magic uses people's names so If a fey knows your name they can do whatever they want to you.

To piggyback on previous responses, a common trick I’ve seen in Feywild games is when introducing a new Fey, they would say “You can call me ArgleBargle, may I have your name?”

The trick is that if you give your name to someone in the Feywild, it is no longer yours.

Probably something about a beings true name giving power over them.

Depending on the way the fey phrased the request you may either have insulted it, or broken a deal. If it asks to have your name and you answer with "yes, my name is <fake name>." You have lied to it and broken a simple transaction. It may even be justified in using ever more harsh measures to extract your name from you, as it has a legitimate claim on it. At least that is the way I would play such a situation for the fey. For me the thing is that trying to outsmart them rarely works, because they know netter in which rules they operate than you do. A answer like "You may not have my name, but you can call me <fake name>. " Should work better in my opinion. Sorry for the wall of text btw. Just being bored out of my mind rn.