You must ensure that your face-down spells and permanents can be easily differentiated from each other. You're not allowed to mix up the cards that represent them on the battlefield to confuse other players. The order in which they entered the battlefield should remain clear, as well as what ability caused them to be face down. (This includes disguise, cloak, and in games involving older cards, morph and manifest, as well as a few other effects that turn cards face down.) Common methods for doing this include using markers or dice, or simply placing them in order on the battlefield.
Basilica Stalker
Because face-down creatures don't have a name, they can't have the same name as any other creature, even another face-down creature.
Turning a permanent face up or face down doesn't change whether that permanent is tapped or untapped.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Nicholas Gregory
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
