You can have a veteran indicator printed on your New Hampshire driver license, commercial driver license or non-driver ID. It costs nothing when you add it during a regular renewal; adding it at any other time costs $10 for a replacement card.
Take a completed Application for Driver License or Non-Driver ID Card, or the Commercial Driver License Application, plus proof of honorable service, to any New Hampshire Division of Motor Vehicles location.
Your DD214 or other official discharge documentation showing honorable service, and a completed DMV application form.