I've known quite a few European families where they've had a tradition of naming their first born after a grandfather - which means that many people in the same family have the same name. They all get around it by calling the people "Big John" and "Little John". I'm not a fan, but it worked for them. It seems to be mainly boys/men it happens to - and they all have the same surname too! Wouldn't want to get the mail mixed up
My DH shares his name with his father. I hate it. His own mother hates it. DH doesn't particularly like it, but likes his name ITMS. Prior to being with DH I haven't had any experience of this sort of thing, but now that I have I know I would never do that to a child. One of my nephews also shares the name, but fortunately its a middle name, and I think that's a nice tribute to his grandfather, but that's as far as I would ever go with it. I think kids deserve their own names.

Like BG and AG, cousins in DH's family have a lot to do with each other, whereas I have a niece via my brother I have never met and will never meet whose name is a shortened version of a girl's name that has always been my favourite and I would love to use, so I think common/similar names among cousins is probably going to be a case by case basis.