Antonyms for the phrase "name the game" include phrases like "hide the ball" or "keep secret." These phrases are often used to describe someone who is being intentionally vague or evasive about their intentions or goals. Another antonym for "name the game" might be "lay all your cards on the table," which implies a degree of honesty and transparency in one's actions. The opposite of "naming the game" could also be described as "playing it close to the vest," which implies that someone is keeping their intentions or strategies hidden, perhaps to gain a competitive advantage over others.