My sister's Jewish husband's family has the same tradition: no child can have the same name as a living relative. Considering that my nephew John (on my wife's side) has exactly two male cousins, both of whom named John, I can see the reasons for the tradition.
Of course, I share the same middle name as my father and his father, whose middle name was from his grandfather. I got my first name from my great-grandfather.
My father claimed he and my mother spent a lot of effort on names, so I don't have the first name as any of my 20-odd cousins I have between my father's and mother's sides.
Information about American English usage here and here. Floating point issues? Please read this before posting. — emc