In America, What is best practice for tagging DMV (Department of Motor Vehicles)?

I am using the latest JOSM. In America, I would like to know what are the proper tags for the Department of Motor Vehicles Here is the Wiki.

For the name I have been using alt_name=*, loc_name=*, short_name=DMV.

For the building I have been using building=offices, offices with an 's'. Combined with office=government.

Finally, in question is amenity=driving_school, I don't feel the DMV as a 'school' since you don't go there to learn to drive. It's more to be tested, drivers licenses, registering vehicles. Thanks