I want to start as a free-lance personal trainer, meaning I don’t want to Incorporate or create LLC.

Hello, fellow trainers!
I am a newly certified by ACE personal trainer, and I am considering training clients in their homes. I do understand the necessity of having a prof. liability insurance. However, as far as business registration-my understanding was that I would have to register my business only if I either incorporate it or create LLC. My intention is, though, to do it as a free-lance trainer (at the beginning, anyway), and I thought that I wouldn’t need to register it in this event.
Is my assumption wrong?
Thanks in advance! I will appreciate all advice I can get
Tamara