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.
Eradicate
The copies must be found if they are in publicly viewable zones. Finding copies while searching private zones is optional.
If you manage to turn a land (such as a Forest or Stalking Stones) into a creature, you can indeed use this effect on that basic land type. Eradicate’s exile effect only looks for cards by name, not type.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Glen Angus
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
