I've heard the word Doc many times on TV, but when I looked up in Dictionary they told me that Doc is " A physician, dentist, or veterinarian.". However, I think Doc is something like Dude. So what is your take?
Can you describe the times you've heard "Doc" on TV? Was it said by a grey rabbit who walks on two legs?
Back in the 30's the famous cartoon character Bugs Bunny coined the expression, "What's up, doc?" It had nothing to do with medical degrees, but was more a casual sort of bravado, when Elmer Fudd was about to shoot him. The expression caught on, and is used in all sorts of situations. I agree that "What's up, dude?" is the same.

Best wishes, - A.

Edit. Sorry, GG, I didn't see your post.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Yes, the expression was "What's up Doc"?
Students: We have free audio pronunciation exercises.
Bugs Bunny was so universally known in American culture that many borrow that expression as a way of saying "Hi there. How are you? Anything new?"

You generally don't refer to other people as "Doc" (unless they are doctors) outside of that expression.
I know Doc Holliday was a dentist when he wasn't busy shooting people, but I'm not sure what Doc Severensen is a doctor of. - A.