Well it depends.
In the old stories this phrasing only meant that you accidentally revealed your full name to the Folk and thereby gave them power over you. With your name they could enchant or lure you, they might even be able to influence your behavior. When you know someone’s name you have a certain measure of power over them. You can do things like catch their attention by saying out loud, referring to them even when they are not present, or even using their influence to bolster your own. But humans don’t have the necessary skills and powers needed to do much more than simple things with a name. Fae, unfortunately, do have such skills and powers. This is why people feared them.
However something interesting has happened in contemporary fantasy surrounding Fae. The idea that the Fae could quite literally steal your name. To be sure, from all that the Fae are able to do in their various myths and folklore, I doubt that such a feat would be impossible for them. Nor would it be at all out of the way to label them as thieves. Not only did they routinely steal food or materials from houses and barns, but they often abducted children, babies, and even unwary adults.
I’ve been putting some thought into how it might work if the Faeries did steal your name from you, or you accidentally gave it to them.
Imagine for a moment that your name has been stolen. Well names are actually pretty easy to come by most of the time. Most people have nicknames of all kinds, and nearly everybody has a last name to fall back on and sometimes an extra name or two between their first and last names. You find that people begin to fall back on these other names that belong to you. If they think hard or are reminded they can probably remember the name that used to be yours, but they might be unable to shake off the feeling that it’s wrong somehow, that it doesn’t belong to you or fit you anymore.
You might even pick up a new name, one you’ve chosen yourself or a new nickname. Most people will happily move to that, thinking in their secret most thoughts that it feels right, more comfortable, but never quite able to consciously say why. Even parents might find this to be true, as years and years of calling you by the name they chose seem to not matter that much as they slip into calling you something else entirely.
But what about birth certificates? Mail? Checks and other official documents that have your name? You’ll still find them. Sometimes official documents, especially new ones, can get the names mixed up or changed and it just stays like that for years until someone notices. Or papers can get smeared if they’re written in pencil, or dripped on by ink or something else. But most often I would imagine they stay the same as they always were. In the eyes of most human governments, it doesn’t really matter if your name fits you as long as all the papers are in order that say its yours. If they wanted to, a Faerie (or even a perfectly ordinary human with malicious intent) could use this against you and commit identity theft to gain even more of what you have for their own. But most of the time I doubt the Fae would care about your finances or anything else unless you did something to offend them.
I don’t think everyone would suddenly and magically forget your name entirely and forever as if it never had been. Mostly because that would cause a huge stir as people suddenly find that a person whose name they’ve known all their life suddenly doesn’t seem to have a name and they can’t remember or find it. People would notice and raise a fuss. And how many people do you know, even casually, that would know your name somehow? Probably a lot of people, to make that many people forget would have to involve a serious amount of power.
While its not impossible that a Faerie would go to all this effort to directly punish you for something that infuriated them, I find it a little hard to believe they’d put that much effort in for it when they could just turn you into a goat or something else of that sort and be done with it.
