Who or whom do I have the pleasure of speaking with?
Both are acceptable. I think that the first is technically the most correct, but it is considered pretty formal. Both are quite formal, to be honest.
How do you politely ask who is calling you?
Say “Hello, this is (name)” to let people know who you are. If you answer the phone and the caller doesn’t give his name, you can say “May I ask who’s calling, please?”.
How do you ask who am I speaking with?
Since the person with whom you are speaking is the object, the correct way to ask is “With whom am I speaking” or ” Whom am I speaking with” Prepositons are preferably not used at the end of a sentence.
Is it correct to ask what is your good name?
“May I know your good name” is a typically Asian way of asking someones name. Perhaps it is being used just as a ‘softener’ or out of politeness, to ask a person’s name. It is INCORRECT. The only way to use “good name” would be in this example.