Very much depends on the family - I’d say that often as not there is a mother or grandmother’s name slipped in there as a middle name at least. A Franco-Welsh couple I know has two girls, one has 2 “new” names the second has a new name (actually, she’s named after me !) and her middle name is that of her grandmothers who share the same name. Another friend is “Anne” her daughter “Annie”. As in the UK there is a move back to more “traditional” names such as Clémence so granny’s name is trendy again !
I’m under the impression that Americans go for the overt “name of the father” more than Europeans in general. That is, despite what it says on the birth certificate, there will seldom be two people in the same family sharing the exact same fist name.