I'm not sure whether Stargirl actually had a name for her "game." You might call it the fifteen-minute game or guess the card game. What she would do, and persuaded Leo to do with her, is pick out a person at the mall, on the street, or wherever she happened to be and follow that person for fifteen minutes. During that time, she would try to guess what kind of card that person needed that day. They would invent a story for the person based on his or her body language, facial expression, things he or she bought, and so on. The didn't actually send the cards to anyone. It was just a way to observe people (or stalk, in Leo's opinion).
Read chapter 21 of the book for more information.
It was called the Card Game. i know