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.