It has name on it

it has (one's) name on it

1. It is reserved or intended for one. Are you sure you don't want a popsicle? There's a cherry one here, and it has your name on it!
2. It is a perfect match for someone's interests or tastes. Susie loves spooky things, so yeah, definitely leave that mystery novel here for her. It has her name on it.
See also: name, on

It has someone's name on it.

Fig. It belongs to someone.; It is meant for someone. A: Is that an extra piece of cake? B: Yes, and it has your name on it.
See also: name, on