Has their names on it - Idioms by The Free Dictionary
have (one's) name on it (redirected from has their names 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."
something has your name on it you are destined or particularly suited to receive or experience a specified thing.
have (somebody’s ˈname on it,
with your ˈname on it (informal) if something has your name on it, or there is something with your name on it, it is intended for you: He took my place and got killed. It should have been me — that bullet had my name on it. ♢ Don’t worry — there’s a job somewhere with your name on it!