**** The information written here is not legal advice and the author of this blog is not your lawyer. These posts merely contain ideas to help you plan and organize your legal research and identify potentially helpful sources of law. ****
State auto insurance laws do require you to carry some sort of coverage on your automobile and you generally do have to prove that you are eligible to be insured in that state by providing the insurance company with documentation of your living in and, if applicable, owning a vehicle in that state. In other words, insurance companies expect that the address you list on your policy application will match the address on your automobile registration and driver’s license, both of which require you to notify state authorities when you change addresses. Also, because the insurance company has legal status as your agent in matters connected with that policy it does need to know where and how to contact you.
To obtain a driver’s license you have to show that you truly are the person you claim to be. The federal REAL ID Act requires states to cross check other identification sources when issuing driver’s licenses. The Department of Homeland Security summarizes the Act at http://www.dhs.gov/real-id-public-faqs and links to the official documents at http://www.dhs.gov/secure-drivers-license-documentation. Each state has the flexibility to design its drivers license identification law in ways that accommodate the homeless and long distance truck drivers and others who do not reside in a fixed location. Some states, for example, accept ID verification letters from homeless service providers.
If your state driver’s license ID law does not yet have a way for you to obtain a license (and, secondarily, insurance), you can contact your state legislature and petition to have the law amended. The National Conference of State Legislatures has lots of REAL ID material for state legislators to read http://www.ncsl.org/Default.aspx?TabID=756&tabs=951,72,110#110 because state lawmakers have been developing these new identification laws for a couple of years.