I don't like twin names that are too similar, but I do think that they should go together. I.E. Addison and Riley, rather than Addison and Emma, or Riley and Leah etc. But I feel that way about all sibling names, not just twin names. I absolutely hate rhyming twin names (Mia and Lia) or boy/girl twins with the b/g version of the same name (Michael and Michelle).
I don't think twins should have the same first or middle name, but it's ok for the middle names to be a variation of each other (Anne and Anna or Mary and Maria etc).