Your landlord is responsible for it, but if not you can do it by telling immigration. Unless its your own home, you will need to do it. You're nearest immigration place should be able to advise.
Hope you get it sorted, your intention was valid, get training, get visa. For that amount of money seems reasonable to expect atleast 1 session per week for 6 months. Yeah there are gyms that offer less, but it's not always so easy to tell the difference.
I belive a comment above about reporting to Thai tourism is for sure a route. I do hope it's just a language barrier, as I have had communication issues, but after using google translate in different ways, got things cleared up.
super smooth, just handed over my passport with the Visa printout, a press there and whatever it is they do behind the desk, done in literally 1 minute.