"Who wants to know?" would normally be said only if you were being pointedly rude. It's a step below swearing at someone, but it's ruder than just ignoring niceties.
Taken at face value, "who wants to know?" is a reasonable enough thing to ask. It ignores the normal polite forms of etiquette, but considering just the bare meaning, we might expect it to be considered no ruder than something like "who's this?" that isn't particularly polite, but isn't explicitly rude either.
But it has acquired much more force, implying "I'm not inclined to tell you" or at least, "I expect you to demonstrate to me why I should tell you, before I do so".
This added forcefulness may well originate in posters like this:
Here, "who wants to know" has the very different meaning: Consider who among our enemies would want to know what you are talking about. And then shut-up.
Just as the phrase "loose lips sink ships" entered the language of English-speaking people in Allied countries during World War 2 to mean "keep quiet about things that might have military intelligence value" or by extension, "I'm not going to talk about that", so "who wants to know?" worked at two levels; it both asked the question (maybe, after all, the person who wants to know should indeed be informed) but also referenced the need for secrecy.
And so at the time while it was brusque its position in etiquette is complex; on the one hand it chided ("you shouldn't be asking me") it also excused ("sorry, I'm not being rude in not telling you this").
And when time moved on it retained this underlying implication of not just asking about who was asking, but suggesting "I am not inclined to tell you this". Hence it seems like slightly-dodgy people in television shows are forever responding to opening questions from the police with "who wants to know?" It's a shorthand for the writer; having the character be a bit rude, but not openly aggressive, is intended to lead the audience to suppose that this person is not perfectly law-abiding but leave it open as to whether they are involved in any serious crime.
Similarly, teenage characters will often use it because [lead character makes exaggerated eye-roll to camera] Teenagers! They're so rude!
Whether the WWII saying is the source of this nuance or not, do not use "who wants to know" on answering the phone if you want to be polite.