[...]may I have your good name[...]?
If someone said that to me at our first meeting:
1. They would get my attention, because this is not the usual way of asking "what is your name."
2. I might wonder, depending on non-verbal clues, if they were talking down to me.
3. If I decided that they were not talking down to me, I would still wonder about the eccentric greeting, but give them the benefit of the doubt. Perhaps they are a bit pedantic?