“May I know your good name?” [closed]

As @tchrist noted in a comment, may I know your good name? sounds overly old fashioned to a native English speaker.

When you're encountering a stranger, a common way to get someone's name is to provide yours first, especially after conversation has already been initiated. This conversation usually goes something like:

Aaron: I don't think I know your name. Mine is Aaron.

John: [My name is] John. It's nice to meet you.

Aaron: Nice to meet you, too.

And then two would shake hands. Generally speaking, it would be rude for John (in this example) to not respond by providing his name.

I often use "I'm sorry, I didn't catch [or get] your name," even when I know it hasn't been offered yet. I preface that with repeating my own name, if it isn't obvious in context.