have (something) to (one's) name
To own or possess something. This phrase is often used in the negative to mean the opposite. During college, when I didn't have a penny to my name, I survived off of ramen noodles for months at a time.
have to your name
have in your possession.(not) have something to your ˈname
(informal) (not) possess something: I’ve only got two dresses to my name.She didn’t have a penny to her name when she arrived here.