Most health care centers will list all their doctors on a web page. So if you do a little research before calling, you can request a specific one (of a particular gender, for instance... doctors come in all genders these days!) You can also request that a second person be in the room for a nudity-sensitive exam. I've been to OB/GYN places where this was the default behavior, but I've also been to places where it wasn't, where you had to *ask* if it is a service you want. So ask, when you make the appointment.
You can also ask ahead of time what exactly that doctor will do during a BasicMed exam, since (clearly) different ones do different things. I imagine that if I were a doctor, I would want to do whatever standard stuff I consider part of gauging the general health of a patient. But if this matters to you, and you don't want surprises, ask.
I'm a woman in my late 40's, so I have been through lots of different medical exam procedures that some might describe as "humiliating". (Yes, rectal too!) It was difficult when I was young, but over the years I have learned to separate the medical necessity of these things in my own mind, and appreciate their necessity. The female reproductive system is a highly complex system with multiple points of critical failure -- some of which I've experienced-- so getting them all inspected regularly is very important, just as for any of one's other organs and systems. A doctor is a professional. (Do not tolerate one who is not!)
In my youth, I moved around a lot, and rarely had a "regular doctor". Even now, I seem to find doctors who then retire and I have to find a new one. So this I understand. Maybe think of this BasicMed exam as "taking a doctor for a test-drive" as someone you can go back to if you're happy with how he or she treats you.
