Many states require fuel tax licenses (sometimes called motor fuel use tax permits or similar) if you use a certain amount of fuel within the state annually, *regardless* of whether the truck is used for hire or personal use. This is because the state is seeking to collect fuel taxes that would otherwise go unpaid if purchased outside the state. The thresholds vary widely from state to state.
Therefore, you must check the regulations in each state where your truck operates. The state's Department of Revenue or equivalent agency will have the specific requirements. Simply operating a non-hire truck in a state doesn't automatically exempt you. If you frequently cross state lines, you'll need to understand the requirements of multiple states.