Rulings

You can't pay Gift of Doom's morph cost more than once.
No player may take any actions between the time you announce that you're turning Gift of Doom face up and the time it's attached to the chosen creature.
If there's no creature you can legally attach Gift of Doom to as you turn it face up, or if you choose not to attach it to a creature, it's put into its owner's graveyard.
This doesn't target the creature Gift of Doom will enchant, so an opponent's creature with hexproof or a creature with shroud may be chosen this way. The chosen recipient must be able to legally be enchanted by the Aura, so a creature with protection from black can't be chosen this way.