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I have always felt that anyone who completes four years of college plus four years of medical school plus a residency of a few years has earned the title of Doctor and deserves to be called by the title of Doctor, or typically, Doctor with their last name, for example, Dr. Johnson.
Having said that, I have met a handful of physicians who, when introducing themselves for the first time, have said, "Hi, I'm Dr. Johnson. You can call me Dr. Johnson or my first name of Franklin is fine, too--whatever you are most comfortable with works for me."
The couple of times I have heard that, I have been very impressed that while the physician has the title, she or he isn't hung up on the title being their identity. I'm impressed that they have earned the title in the first place, but I'm even more impressed that they don't need me to feed their ego by using the title in addressing them.
So, in my case, you can call me, "Sir Franklin Johnson of Riverton, Chief Supreme Mucky-Muck Head-Honcho, El Numero Uno" or you can just call me Frank, whatever you are most comfortable with works for me."