As far as the identity of the caller not being the business of the person answering the phone, the fact is that (in business) many employees are instructed to get the name of the caller before putting the call thru. It’s part of their job. Many are also instructed to find out what the call is concerning.
Then they need to do their job and enquire by saying 'Who's calling please?' That's accepted phone etiquette and I don't see anything wrong with someone having to say that.
That's true and I do that at work. I'm a receptionist, and most calls, I just need to know where to transfer the call. I'd rather they started with "I'm checking on my order," or "Customer service, please." I hate calls that start with "Thus is Bob from ABC Store, Account 123." - then silence.
Me: "How may I direct your call?"
Bob: "Customer service."
Me (out loud): "Hold on, I'll transfer you." (To myself): "Well, why didn't you just say so?"
If a call if for a higher-up, I do have to screen. Again, nothing wrong with not IDing yourself right away, as long as you're prepared to do so when asked.
Two incoming calls I've dealt with:
Caller: Is CEO there?
Me: May I ask who's calling?
Caller: this is John Smith from ABC Company. I'm calling about (gives reason for call here).
Caller: Is CEO there?
Me: May I ask who's calling?
Caller: Mary (silence)
Me: What is this in reference to, Mary?
Caller (Mary) Your phone service.
Me: Where are you calling from?
Mary: St. Louis
Me: I meant what company?
Mary: XYZ Company.
Me: And what us this in reference to? (I need more than just "phone service and I can't think of a nice way to ask "what about it?" - I'm hoping repeating the question will be a hint that I need more detail.)
Mary: Your phone service.
Me: But what is it in REFERENCE to?
Mary: Is CEO there?
Both cases, I go to CEO with as much information as I have. Which call is more likely to go through?
My point: you don't have to ID yourself right off the bat, but please do so when asked. Don't make me have to drag it out of you.