Referring to some attribute of an inanimate object — use "who's"?
It is wrong, but not because a daemon is a thing rather than a person — "who's" doesn't indicate possession, it's a contraction of "who is". You need whose, which is a possessive pronoun and adjective, like his, hers, etc. So, just like you'd say "his name", you'd say "whose name", or "its name".