Mica "Got That Dog In Her" Kobold

looked out the window and this guy was munching

Don't panic! All is not lost.

For starters, point out that it was not your name to give when you gave it to them; you gave your name to someone else long, long ago. You don't recall who--probably a family member or friend of such back when you were four or so, but really there's no telling.

If they somehow have successfully taken ownership of your name despite that, point out that, as you now need a new name, you have decided to name yourself after your new idol: the fae you're speaking to. Truly, you are honoring them by naming yourself after them! It would be rude for them to refuse this. Imitation is, after all, the sincerest form of flattery; how could they possibly accuse you of being duplicitous?

Should they refuse it anyway, consider that what they truly own is more akin to intellectual property than a tangible object. Consider torrenting your name off Limewire or something, or whatever the kids are using these days.