If you literally want to create a game using pen and paper to play with a partner, here are common "Girlfriend Games":
The title story is a psychological thriller about a couple who play a provocative "game" in bars where the woman pretends to be a stranger to lure in men, testing the limits of their relationship until it spirals out of control. The Girlfriend Game
Each person writes a character’s name on a piece of paper and sticks it to the other's forehead. Use yes/no questions to guess your identity. If you literally want to create a game