Alhammarret, High Arbiter

You choose one card name, not one name per opponent.

Alhammarret's second ability happens as Alhammarret enters the battlefield. No one can cast spells or activate abilities between the time a card is named and the time that Alhammarret's last ability starts to work.

Although spells with the chosen name can't be cast, permanent cards with that name can still be put onto the battlefield by a spell or ability.