It's difficult to record several people talking with just one microphone, because using just one microphone, it will have to be omnidirectional (i.e. capture sound equally from all directions) and be placed at an intermediate distance between all participants and this can cause three problems:
- Lack of separation of ambient noise from useful sound.
- It's hard to balance sound volume from the different persons speaking.
- Reverberation, i.e. sound reflection from the walls, ceiling and floor, will also be captured and that can produce a muddled sound, sometimes even preventing intelligibility of speech.
So, it's not by chance that they use lavaliers and overhead mics with boom arms to capture sound in professional situations :-)
Having said that, if you have a relatively quiet room with not too many sound-reflective surfaces, and want to give a try, what you need is an omnidirectional microphone with a neither too low nor too high sensitivy.
A USB "conference room" microphone like this one (I'm not recommending any specific brand or model, I just provide the link to exemplify the type of equipment) is probably a good alternative (although you don't need the call funcionalities) as a music/speech oriented dynamic mic has normally a cardiod pickup pattern. There are a lot of nice USB condenser mics that allow omnidirectional capture, but a condenser is probably too sensitive for your application (you don't want to hear every breath or clothes crackling of your patients).
If you can, try to provide as much isolation as possible (bear in mind that even outside street noise, a creak of a chair, people's feet scratching the floor, etc. will be competing with the actual conversation) and as much room padding as possible (pillows, bookshelves, rugs, carpets on the walls, etc. will help).
It's possible that you may achieve satisfactory results for what you need, but for the explained reasons, don't be surprised if you don't.