Etrata, Deadly Fugitive

A permanent that turns face up or face down changes characteristics but is otherwise the same permanent. Spells and abilities that were targeting that permanent and Auras and Equipment that were attached to that permanent aren't affected unless the new characteristics of the object change the legality of those targets or attachments.

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.

If you cast a spell "without paying its mana cost", you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the card has any mandatory additional costs, such as that of Demand Answers, those must be paid to cast the spell.