That shows a supreme lack of imagination, IMHO. Which is not illegal, by the way. It just reminds me of My Big Fat Greek Wedding, in which 50% of the men in the family were named Nik, Nikki, Nickolas, Little Nikki, etc. There are squillions of names out there. Why do this? I can see using a common family name as a middle name that you don't actually call the child, but to have a family get together and have multiples of several names is so easily avoided.
The OP cannot stop her SIL from naming the baby anything at all. She cannot order her not to. But if they are first cousins and HER family views it as odd, then it's not a good or considerate thing to do. If someone did that in my family, I would not take kindly to it.
When we wanted to name DD after my mother and my sibling had already used that name, (but the child didn't actually go by that name) I asked if it would bother them if we used the name. They said no because they didn't even call their daughter that. They said if they called her by that name it would have bothered them and I said if that was the case, I'd have never considered using it. The name has been in our family for several hundred years, but used one generation at a time.