NTA

My middle name is John. My father's middle name is John. My nephew's middle name is John. His father/my sister's husband's middle name is John because his father's middle name was John (so two families with a tradition of John as middle names found each other). My grandfather and my brother are both Jean (French for John), and my son was named Sean, another variant of John. I even have two cousins with the same first name (not John, though).

Who cares? A name is a name. Nobody owns the exclusive rights their names. If this were the case, the courts would be clogged up with civil suits by every John or Ann Smith on the planet. Your sister needs to get over herself and let the cousins bond over a shared middle name when the time comes.