This can't be used as a counterspell. It will have no effect on spells which were on the stack when it was cast, nor on those cast in response to it.

Players may cast spells while Conjurer's Ban is on the stack. Only after all players pass priority does Conjurer's Ban resolve, and that's when you name a card. Once you name a card, that card can't be played in response.

You may name a land card to prevent it from being played.

Conjurer's Ban only affects cards. A copy of a card (for example, one created by Eye of the Storm isn't a card, so it can be played.