Your name must be unique, and not deceptively similar, to any other trademarked name or business. It is also required that your name not be used to intentionally misrepresent the products or services you offer. For LLCs, nearly all states will also require you to add a signifier of your limited liability status, such as "LLC" or "L.L.C." to the end of your company's name. You may be able to operate under a name other than your formal LLC name by applying for and using a dba.
In some places, dog walking alone can be a very profitable business. Those working from 9 to 5 either do not have time to walk their dogs before leaving the house or just prefer it if someone comes in to let them out of the house for some exercise. Also, dog walking businesses that offer additional services are becoming increasingly popular. Consider also offering: