A marine motor assembly for a watercraft and a cover for a marine motor assembly. The assembly includes a housing; a motor disposed in the housing; and a propulsion device operatively connected to the motor. The housing includes a housing portion, and a cover selectively connected to the housing portion. The cover includes a cover body connectable to the housing portion, the cover body covering at least a portion of the motor; a noise dampening material layer disposed on an exterior side of the cover body; and a surface structure connected to the cover body, the noise dampening material layer being enclosed between the cover body and the surface structure.