Well, I liked the idea of Luke being reknown for his surname, along with the DS destruction. Surely, this would leave the emperor standing as a fool, when he says "he's the offspring of anakin skywalker"... but if we left the 1980 dialogue, it could work.

I insist, this "contradiction" (which is never officially stablished) of watching the saga in order and saying "hey, anakin was such an important figure, and 20 years after, other Skywalker appears and no one seems to relate them, or remember Anakin's great deeds during the CW" could be arranged in the prequels by makin Anakin some Mr Nobody (?), though for me it would be better to get it fix in the OT