"Who should I say is calling?"
ell.stackexchange.com/users/66909/JeremyC
As far as politeness goes, the following examples, along with what JeremyC has already suggested, would also be some of the safest ways to ask people for their names when talking with them over the phone:
Could you please tell me who I'm speaking with?
May I ask who's calling?
Would you mind telling who's talking?
ell.stackexchange.com/users/6450/Michael Rybkin
In my experience, "Who is this?" is generally perceived as more polite than "Who are you?" or similar.
I don't have a good reason for it.
There are other more-polite forms, as noted in the other answers, but "Who is this?" is direct, reasonable, and unlikely to offend.
ell.stackexchange.com/users/6186/R.. GitHub STOP HELPING ICE
May I tell X who is calling? has always worked for me.
If they refuse, I hang up.
ell.stackexchange.com/users/64237/Jeff Morrow
There's not one perfect answer for every situation.
If you don't hear the name the 1st time, just say that.
Or, if the caller just gives his/her 1st name, state that you need the last name as well, and the reason why.
I encounter this often.
Although I am a native English speaker, most of my callers speak Spanish.
So, I am confronted with two problems:
First, the need to know the full name of the caller; and second, the fact that I am not trained in the culturally-appropiate way to ask my client's identity in Spanish.
(And the most appropriate way to ask this, may vary from country to country, anyway.)
My advice is to listen to the caller, and to respond in a way that seems correct for that situation.
Your tone of voice, and your attitude, probably are more important than the exact words that you use.
ell.stackexchange.com/users/71294/user71294
Say, you're working in a company. The phone rings and you pick it up. On the other line, someone wants to speak to one of your co-workers. You want to tell your co-worker who this person is.  I think asking "May I know who you are?" is a bit rude? What's a more common or softer alternative?
What's a polite way of asking "who are you?" on the phone?
ell.stackexchange.com
<phrase-request><politeness><informal-language>
ell.stackexchange.com/questions/159621
ell.stackexchange.com/users/43585/alex
"Who should I say is calling?", "May I ask who's calling?", "Would you mind telling who's talking?" and "Could you please tell me who I'm speaking with?" are all polite questions. However, the more direct "Who is this?" is also  reasonable. "May I ask who's calling?" or "Could you please tell me who I'm speaking with?" are both acceptable ways of asking. "Who is this?" is more direct, but unlikely to offend.
"May I ask who's calling?" or "Could you please tell me who I'm speaking with?" are both acceptable ways of asking. "Who is this?" is more direct, but unlikely to offend.