Look, I'm gonna just go ahead as say, that I have like no opinion on what other people do with their lives. Y'know? I've got no skin the game and just think as long as no one is getting hurt, life will be dream. That been said... I do have skin in the game with mytholgy and I do have a bit of a confusion with the whole, 'fae will take dead names off of your names' things.
Let me explain. Fae are not your friends. Even friendly fae are not your friends. Fae are the creatures that will inite you into their house before trying to find your name and keep you as a 'servent' or like, take out your eyeballs and pickle them for later, or so on... You know? They never just be nice, because fae is so far from humanity that normal human ideas are alien to them. That and fae are more or less not thinking of humans as humans thing of ourselves. They don't hate humans, but they sure as hell don't look at humans at the same level of importance as humans look at ourselves.
Another thing is that names link to your soul, that is why names in folklore, fair tales, myths and have names as very important things. More or less with things like demons being able to be ordered around if you know their true name, or things like H.P. Lovecraft using the theme of true names and so on. In other words, a humans dead name would be the equavilent to any other entities false name. Like, you could call Lucifer the devil, the great dragon, the enemy but that doesn't remove the fact that his name is Lucifer. And since humans are usually the ones who give other humans names, with some culutres also having the idea of a true name, it's more likely that dead names have no sway over the actual person soul. Which means, there is no real reason for Fae to want it.
Look, as I said before, fae are not your friends, meaning they have no reason to just be a bro or gal pal and free you from a dead name, but that also means that most of their actions are for self profit or a greater profit. And since I've already argued that a dead name would be the same as a false name and thus have nothing to do with a humans soul, which means it's fucking useless thing for a fae to do!. Fae are the types to do things like kidnapping human children and replacing them with fae childern or elders (depending on the taller of the lore of changelings), but you get it, no?
Like realistically I would assume a fae either has something else planned or just flat out wouldn't need or want a dead name. In my opinion it would make the most logical sense for the whole thing to be backwards. I.E, a person with a dead name lying to a fae by offering their dead name instead of real name, or having to give up on their dead name 'cause a fae knows it.
Just... We keep making these monsterous creatures seem less and less monsterous and try to like, anime girl them. Vampires in og myth were terrifing and more like modern day zombies. Werewolves had nothing to do with the moon. And while I'd be the first to argue about how I love reimaginings of these creatures, like the kind in VTM, WTA and so on. The only reason it worked is because the original through line was the same. Vampires will always be pradatory, werewolves are always part of the natural beast in humanity and so on.