I would suggest naming your PT business something congruent to your location and service based on SEO. I am sure you will have a website and you definitely want to near the top on the search rankings. Pick a niche with whatever SEO combo that is most tailored to your location and service!
Do you have a membership management program to help launch your business?
Check mine out at http://www.gymmembermanager.com/
Best of luck on your new venture!