Caius the Mega Monarch if targets 2 cards inflicts damage twice?
The opponent will take 1000 damage.

Think of it like this; if you tribute a dark monster, you modify the activation cost (i.e., instead of "Target 1 card on the field", it becomes "Target 2 cards on the field;"). The effect simply states "Inflict 1000 damage to your opponent." This means that the modified effect would become,


  banish them, and if you do, inflict 1000 damage to your opponent, then, if any of those monsters were DARK Monster Cards, banish all cards with the same name as those DARK Monster Cards from the hand, Main Deck, Extra Deck, and GY of the player who controlled them.


As the 1000 damage is not per card - simply an effect to itself - the amount remains the same.