The Percy Jackson reference was merely a coincidence. I was typing and saying the names out loud, and when I said "Peresea," my cousin mistook what I was talking about, and instantly assumed I was talking about the book/movie...The other two, with their mythological godliness references, don't really fit at all, unfortunately. :\
EDIT: Another variation could be Neumi (Umi, being ocean in Japanese) I dunno, which sounds better?
Neomi (Nee-ah-mee) or Neumi (Nee-oo-mee)?