have somebody's name on it
have (one's) name on it
1. To be reserved or intended for one. Are you sure you don't want a popsicle? There's a cherry one here that has your name on it!
2. To be a perfect match for someone's interests or tastes. A: "This mystery novel really has Susie's name on it, doesn't it?" B: "Oh yeah, she loves spooky things."