What if Darth Vader is a borrowed name from another sith?

Like once a sith is vanquished, the victor assumes that identity? It consumes him figuratively and literally(as his moniker even changes)

He ceases to be Anakin Skywalker and becomes Darth Vader.

So the 1-6 audience would still think Anakin died because "Darth Vader" was still around.

But then once ESB hits, it would be "what? but he's not Luke's father because he died!". "Yeah but maybe Anakin really did survive, kill Vader, and assume his role?"

I don't know. Throwing stuff at the wall.