Very well indeed- but that's not the answer. Or rather, it's a lot of the answer- so far,
most of the guesses are correct, but as I said there is a "trick" to this riddle, and the identity of the speaker depends on that.
If everyone gets really stuck, I'll supply hints as to the nature of this trick. In the meantime-
"Like-named" doesn't refer to the (no, not necessarily literal) "maiden" having a name similar to the person in the line above her. What it does refer to... is also part of the "trick".
Edit: I think I should also add that your suggestion of Tuor, and the reasoning behind it, is
thematically appropriate.