How to Patent a Business name in the US?

To use the name at all - you have to be registered as dba in your state. This is not to "protect" your name alone makes it legal to use... For a brand name, go to the U.S. Patent Office and Trademark Office. www.uspto.gov

Patents are for inventions
 
Copyrights are the creative works such as books, music, graphics, art. Trademarks are names and slogans.