I’m guessing there could be some sensitivity based on local dialog. Things I would consider: You don’t need a terribly killer website name as it’s mostly local advertising. However you need to be careful that the name is not invisible on the internet. A friend was setting up a business for home products for beach/shore houses. He wanted to call the company Barrier Sound, however I informed him the first 200+ searches on Google turn that around to “Sound Barrier” and that he would be deeply buried.
I’d suggest you do some research first, give me the names/websites of the top 4 or 5 trainers in your area.
I should be able to offer some assistance by looking at what they are doing.