I don't think anything *must* happen with the names of children in the same family, twins or not. If I had kids their names would "fit" because I like the same sort of names the most, but it's not as if I think it *needs* to be that way.
Right now if I had twin girls I would name them:
Edna ElizabethJoan Margaret
Motherland fatherland homeland native land.
It’s all the same. What the hell good to you
is your native land after you’re dead? Whose
native land is it after you’re dead?
Dalton Trumbo, JOHNNY GOT HIS GUN