For whatever reason, many surgeons are hesitant to get a presence on Facebook. Some think they may get forced into giving medical advice on Facebook if they are on it. They need not worry.
Many times the person running the social media presence of a doctor is not the doctor anyway. You need not respond to Facebook posts if you don't want to.
There really is nothing to fear. There is however much to gain... A Facebook site gives you one more way to be found, makes it easy for your happy patients to refer you and give you a valuable link back to your own web site that helps you with the search engines.
An example of a good Facebook page for a Doctor is below.
https://www.facebook.com/DrGibby
(Doctor Diane Gibby is a plastic surgeon in Dallas who specializes in breast augmentation.)