In the "Things I didn't know existed" department is the "Brand Book" an official listing of registered livestock brands usually maintained by the state Department of Agriculture. Some states have online directories but there are also physical books.
To answer an obvious question. Yes people still brand cattle. Most ranchers also use ear tags for record keeping but the brand establishes actual ownership.
At time of writing Colorado records ~30,000 brands while Missouri has ~5,000. If you are interested in registering a brand in your state go consult a local search engine.