The most correct form are these (and they are valid for both the case you write about). "Come si chiama?" ("lei" is simply implied) "Lei come si chiama?" "Come si chiama, Lei?" "Come si chiama, lei?" The upper case is used to make the written more formal. Is it clear ?

That is right but I have to add something that is Lei como si chiama? Is the polite way to ask the name of an stranger elder What is your name sir / madam And lei /lui como si chiama? Is the third person singular he or she What is her or his name?