I think any professional should consider their public image and how it’s perceived.
Gender doesn’t matter. Men & women should carefully consider the content published on social media.
They should separate their professional and private accounts. Dr William J Burns on Facebook. Bill Burns could be the private account.
That’s up to them. I don’t particularly care. I’ve never looked up a doctor or other professional on Facebook. Google gives me a phone number, office address, and that’s all I need.