Depends on where you live. In Wyoming, the state's Dept. Of Ag maintains a brand registry.
If someone wants to brand their livestock, they either buy the brand from it's current owner and notify the state of new ownership, or they get a list of abandoned/un-used brands and apply for ownership, or they create their own and apply for approval. Once a person owns a brand there is a fee required to keep it current.
When I was in Indiana years ago, the owner of a farm wanted to brand his cattle. He designed a brand, notified that state's department of ag, and was told they didn't have a registry. They suggested he notify area sale barns of the brand so they would know who, most likely, should be involved in the sale of cattle.
Just pointing out how it can vary between states.