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. If answering the phone and someone says: "hello, is that nadia" "Hi! yes, this is Nadia" (almost always, the person will immediately introduce themselves) but if you do want to ask, you can just say: "who am i speaking with?" or "who is this?"

Hi! I'm Ron from New York, USA. I am happy to help you improve your spoken English if you need help. I also love to make new friends everywhere in the world! If you want help, please add me to Skype so we can chat better: ron.jenkins86 Thanks and have a great day! :)

Whom do I have the pleasure of speaking with? <- more common

Well, to be strictly correct grammatically, you should use "both" in both instances, but to be honest, hardly anyone does (including me unless I'm feeling especially fastidious!)