Since the tiny home is on a trailer then however you title and register the trailer without a home on it, or the trailer with a home on it, with the Department of Motor Vehicles is how it will be.
You might look at not registering it at all and just get a temporary move permit anytime you need to move it from one place to another.
Unless it can qualify as a modular or mobile home in your state then it is unlikely that your municipality will ever qualify it as a permanent residence while on wheels.
All of this is highly dependent on the laws, regulations and ordinances of your local city, county and state.
Hopefully this is helpful.