And you should do so the most professional way you can, dispite personal preferences. And so I think your boss is right to call you on it.

People in my office say "Well who is this?" All the time and it really sets a bad tone to the whole conversation.

I generally try to go with "Who may I say is calling" or "May I tell her/him who's called?"

If someone's called and start into their life story before identifying themselves sometimes I may catch them with a "And you are?" I think its a subtle but not totally rude way of saying "you were being rude by not telling me who I am speaking to before now"

But again, whatever your actual job, when you talk to people as a representative of your employer, you need to hold yourself to their standards. Its an unwritten rule of employment.