Yeah, I think ultimately Zelda is too much of a bleeding heart to just kick her out, especially if the girl gives away that she's kind of expecting to be named by her. Though she'll make sure the shinki is aware that she has her own duties to attend to back in her world, so she won't be here to act as a goddess forever.

If the shinki is still cool with all of that, then she'll name her. I could handle NPC-ing her maybe? Kinda like how some missions offer an NPC cracked shinki as a reward. I would just want like... a document or plurk paste or something to refer to regarding things she knows, maybe some basic experiences she's had before the cult compound assault, etc