Telephone rings. I answer: "Hello?"
Me: "Yes, hello?"
Caller "Don't you know who this is?"
I have one particular friend, "Jane", who always does this, and others do it as well. Jane doesn't have a terribly distinctive voice -- particularly not just with just the word "Hi". She's not a very close friend -- I see her maybe once a month, or someone who it would be a wonderful surprise to hear from, which might make it more justifiable to be asked to guess, perhaps.
It may be that she telephones most friends on mobile phones, which would normally show her name if it was programmed in, but she calls me on my landline. Mostly I do know that it is Jane calling, although I refuse to play the game when she does this every time. This evening when she rang and tried to play the guessing-game I just said, "Someone who doesn't like to identify themselves when they ring?"
I really don't know what a polite response would be if someone insists on doing this.