May I know your name?

I don't use either of them.

What is your name, please?
May I have your name, please?

If I'm on the phone with a customer service representative, I might say, "Can I get your name, please?"
If I'm at a friend's house and talking to a child there, I might say, "And what's your name?"
If I needed to check a list of names for people checking in to an event they had registered for, or if I had to start of list, I'd use "May I have your name please?"
If I'm talking to a stra

Kelly TanMay I know what your name is?May I know your name?

These are not common but, might be used in situations where the speaker is trying to be excessively formal.

The suggestions in the other answers could be used in situations where someone needs to speak formally, just not excessively so.

In simple, informal situations people just ask

Native English speakers do not ever say either one of them.

Whenever I hear someone ask if they may know my name, I think to myself that yes, they may know my name or they may not, but that is not a way to ask for it. I don't say that to them, but just tell them my name. Preferably, they should ask "can I have your name?" or "what is your name (please)?

Califjim,

What difference does it make when the question was asked? I hear the question almost daily, and today - even though I have a couple of reasons why they do it - it got me to ask on line, which got me to this site. Although it's a question that gets asked often, after so many years the OP probably already has their answer.

There is also the thought that now anyone that com

Yes,you might.My name is Fahim