Who is the coolest Doctor in the hospital?
Q: Who is the coolest Doctor in the hospital?A: The hip Doctor!
This is another "Dad Joke" The definition of dad joke is pretty loose, however generally speaking lame puns are certainly in the domain of Dad Jokes.
The humor in this joke is derived from the fact that hip has two meanings. According to google: "a projection of the pelvis and upper thigh bone on each side of the body in human beings and quadrupeds", and "following the latest fashion, especially in popular music and clothes".
This joke is therefore a pun - the doctor that deals with people's hip is also the trendy doctor.
I can't see any deeper humor than that in this joke.