The short answer is no, if you form an LLC or incorporate a company it means that a corporation or LLC cannot be filed using the same name in that state of formation. However it does not preclude anyone else from incorporating that same name in any of the other 49 states. What we often suggest to clients before submitting an order is that they search to see if the corresponding URL is available. In this day in age most companies will own the URL of their respective company.
If you form a corporation or LLC in a state and want to protect the name from being used by someone a trademark application will need to be filed with the United States Patent Office. If you own a trademark then it would provide you with legal recourse if another company in the same industry were to initiate a business using the same name.