As an entrepreneur, you are wise to seek a second opinion, especially in matters of intellectual property. Your attorney is right to the extent that you don't need to trademark your business name in order to use it in another state. Business names are determined by the Secretary of State of the state you're based in.

For the most part, once you choose a name, it's yours. But that also means that companies in other states could have the same name as yours. However, if you're looking to expand to other geographic markets, you will want to start developing goodwill through consistent branding. Speak to an intellectual property/trademark specialist to discuss how best to handle your branding roll-out and protection. Like consulting with doctors, it never hurts to have a second opinion.