As progressive as NH is I don't know what took them so long.
A close friend of mine who transition 8 years ago in NH, had Male on her license after she transitioned with her female name. When she went to renew her license 3 years ago with her new female passport (and still pre-op, but blends really well) she was surprised when the DMV clerk said: "Oh look, they have the wrong gender on your license, let me correct that for you." She responded with: "Oh, I didn't notice, thank you." And then she had female on her license.