My (new) dentist seems to be very accommodating with the large green tanks I use. She allows me to position it close by so I can make adjustments if needed during the procedure. I learned it is difficult to breathe through your nose with your mouth wide open. 😳 She will stop for short breaks but will not adjust the tank flow for me. I always go with a full tank - just in case.
Our only challenge is getting the head and neck adjustments just right. I find breathing a bit easier with my head propped forward and upward. She could probably work better with me balanced head over heels - upside-down and backwards. Oh well!
Unless you are wearing an oxygen mask, it shouldn't be a problem. A nasal cannula doesn't go in, or near your mouth, so should be easy for the dental tech to clean your teeth if you have it on during the procedure. Then again, if you are on 2 liters, and you'll be sitting still in the dental chair, can you take off the cannula and turn off the O2? Less stress all the way around. Either way, I wouldn't worry about it -- I'm sure the dental tech has experience with working around oxygen. Good luck to you.