My wife is a retired surgeon so I have been around docs for the last 35 years. I've sold both custom and from stock kitless fountain pens at medical society charity auctions to them as well and nobody has ever asked for anything that resembled an MD logo.
Believe me they are all proud of their accomplishments and might appreciate a bobblehead to put on their desks, but when it comes to personal items, what they don't want or need is something that explicitly spells out MD in bold capital letters. It's on their jacket and ID tag all day at work. Let the BMW do that on its own.
A medical student or first year resident/intern might like a caduceus clip, but someone in practice would, I think, really appreciate a simple, straight forward, high quality pen, perhaps in school colors, or even basic black. IMHO This is not something to overthink or get fancy with.
FWIW,
Bill