Most people of good taste very much dislike being asked their names. To say "What is your name?" is always abrupt and unflattering. If you want to know with whom you have been talking, you can generally find a third person later and ask "Who was the lady with the grey feather in her hat?" The next time you see her you can say "How do you do, Mrs.—" (calling her by name). Does the author use a consistent tone in the passage?