Exile target nonblack creature. Search its controller's graveyard, hand, and library for all cards with the same name as that creature and exile them. Then that player shuffles.
A face-down creature has no name, so no card can possibly share a name with it (not even other cards with no name). If you Eradicate a face-down creature you will still search its controller’s library, but you won’t be able to exile any cards from that library.