Personally I think that any of the current Tabata style classes out there are considered HIIT classes (very different form the original study Dr. Tabata performed). For this reason alone you can call it what ever you want. You can create classes similar to the “Tabata” style classes which are taught around the country without even using this title.
In college we called in interval training. When someone told me about and explained Tabata, I thought that’s been around for MANY decades; it’s interval training. The type of intervals are based on the goals for each workout. That being said…from the comments above not sure of the legality, but maybe better off safe and not call it Tabata.
Good luck, sounds like you have a great group 🙂