As was mentioned, you question is beyond a tax question. However, most states require a registration an LLC if business is physically operated in that state.
That means if you are solely physically working in New Mexico, yes, in most cases that is likely the only state you need to register the business.
But if you (or your employees) are working in other states, those states may require a registration.
But the laws vary from state to state, so you'll want to look into each state's rules and/or consult a business lawyer.
