The man in the OP was rude and the pastor should have been told.
Also, not every business should identify itself first. If my doctor, lawyer, CPA, calls they don't know who is answering the phone. They need to ask for me without identifying themselves. I may not want my husband, sons, son's friend answering the phone to know my business.
That is a great point. I also think caller i.d. (or maybe people assuming everyone has it) may have changed how we handle phone calls.
Thinking back on it, I realize that my doctor's office has always asked to speak to me first, before identifying themselves. But then so do many telemarketers. I recognize my doc's # on caller id, so I don't ask who is calling because I know, so I just tell them it's me and we get on with things. If I don't recognize the number, I ask who is calling and if it's some scam or whatever I tell them "she" (i.e. me) isn't available.
I called my friend the other day and when she answered I said "Hello, Friend? This is Softly." She said yes she knew - I didn't realize her phone had caller i.d. We had a laugh about it.
Family and friends know my voice, and jump right into the conversation after I say "Hello?" with a "Hey Softly how's it going?" etc. I can usually in turn recognize their voice (could do that before caller i.d.) and we just talk - no introductions needed.
However, barring special situations I think you can never assume a) that when calling you will get the person you are looking for, or b) that the person either calling or answering knows who you are.
So if you are calling a stranger, it's good to both introduce yourself and confirm who they are - in whatever order feels appropriate. Whether it's "hi this is myname may I speak to so and so?" or "Hi can I speak to so and so? This is myname." I get including your business affiliation as necessary, but I don't think it's prudent or polite to state your actual business/reason for calling unless asked directly or until after you've confirmed you are talking to the right person.
I don't think it is rude to ask who you are calling/speaking to or if soandso is there, especially if it is an unfamiliar number/first time calling, because you could have easily misread or misdialed etc.