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. We may not have had a nickel to our name growing up, but my family was so full of love that it never felt like we wanted for anything. They used to be so well off, but now that their business has closed, they have nothing to their name.

have to your name

have in your possession.