Yeah, that's the crux of the question, etymology. It's pretty common in countries that have a background in immigration, like Canada where I'm from. Like someone might say, "oh it's a Scottish name and my last name is Estonian." It's a super normal and kind of fun question here.
Well, no, that would be "mikä sinun nimesi on?".
"Millainen/minkälainen" (what kind of) is used to ask after the kind of quality, type etc. something has.
"Millainen päivä sinulla oli?" - What was you day like?/ How was your day?
"Mukava." - A nice one.
"Millainen nimi sinulla on?" - What kind of name do you have?/What is your name like?
"Minulla on perinteinen suomalainen nimi." - I have a traditional Finnish name.
It's a bit of an odd question, to be sure.