Some people confuse choosing a business name with choosing a type of ownership structure, such as a corporation or limited liability company (LLC). But you can't just tack "Inc." or "LLC" onto the end of your business name and start calling yourself a corporation or LLC.
First you must form a corporation or LLC, and to do so you've got to follow certain filing procedures to register the new type of company with your state. For more information on the various types of businesses, see Learn About Business Ownership Structures.
For step-by-step help in choosing and registering your business name, see The Small Business Start-Up Kit: A Step-by-Step Legal Guide, by Peri H. Pakroo (Nolo).