have your name in lightshave/see (your) name in lights
informal to be famous for your work in film, theatre, music etc..
She accepted the few badly-paid roles she was offered and continued to dream of seeing her name in lights.
have (one's) name in lights
To be well-known due to one's work in show business or the arts. Alice has always dreamed of having her name in lights, so I'm not surprised that she's making her Broadway debut tonight.
have your name in lights
1 (of an actor or performer) have their name displayed in lights outside a theatre, concert hall, etc. 2 be famous.