All of my answers to this question depend on how closely related the parents are to you. If it were a distant relative or friend and I were already pretty firm on using the name, I see no reason to ask permission... just use it. If it's your sibling who has a child that name, though, I wouldn't even consider using the same name. In my opinion, cousins shouldn't have the same first names. They are too often in the same circle of discussion at least and there will have to be some distinction (big bob/ little bob etc) and that is uncomfortable for everyone I think.
From personal experience it irked me a little when it kinda happend to me. There are only two grandkids on my husbands side. Mine is 5 and her new girl-cousin was just born to my husband's sister last year and they gave her a name that sounds like my kids unusual name, but is slightly different. (like if my kid's name were Belle, they named their kid Bella).
I'll get over it, but it seems that of all the names available in the world, the new parents could have some originality and not use something I picked first. I wasn't flattered at all & saw it more as a kind of competition thing because grandma was super-fond of her only grandkid (mine) & it seems as though they feel like they had to mimic her to get some of the love or something. I just thought it was bizarre (and to make it worse they have almost the same birthday!) so we've got only two grandkids years apart but with nearly the same birthday and nearly the same name. and no, they didn't ask first, but if they had I couldn't have said no. Even though I don't like what they picked, I would never tell parents how to name thier kids. I might have tried to dissuade them though, as I think the result is a little too bizarre. If it had been my husband's cousin or friend though, I wouldn't have cared less. It's just that being cousins with someone of the same name is a little too close for comfort in my opinion.