Yes, any person--including a sole proprietor as well as LLCs or corporations (which qualify as being "people" for certain purposes)--may own intellectual property, like trademarks, tradenames, copyrights, or patents. So assuming the mark or name is copyrightable (go to the U.S. Patent & Trademark Office, or PTO, website for excellent information on the subject and some tools that can help you determine trademarkability), you can do this.