If you activate “Dark Designator” and your opponent says he/she has no cards in their Deck of that name, you may check the Deck to verify.
You cannot declare a nonexistent card for “Dark Designator”.
Your opponent must show you the card added to his hand.
Netrep Rulings:
If the player required to search for the Monster Card designated by “Dark Designator’s” effect does not have the specified card in his/her Deck, the controller of “Dark Designator” may search the opponent’s Deck to verify this.