In the context of the series, the idea is that you can't tell at the end of SITH whether Anakin or Vader is taken out of the lava. When he is put into The Suit (meaning what we consider the Darth Vader suit), he identifies himself to Palpatine as Darth Vader, and that is how the name and the suit come to be associated.

What a first-time viewer watching sequentially would then discover in Empire, is that it's actually Anakin in the suit. It would be up for interpretation as to what motivated Anakin to do so -- most likely a desire to leave his former self, his "weaker" self, behind. In fact I'd probably throw a line about taking on a "Darth" title and leaving your old life behind somewhere in the big confrontation at the end of CLONES, just to make it resonate a little more.

(In Jedi, Palpatine has clearly known the truth the entire time, but I think it's within his character to play along -- as long as Vader does his bidding, he doesn't really care what he used to call himself.)

If your first exposure to the films is 4,5,6,1,2,3, then you'd know who is in the Vader suit at the end of SITH -- as you do with the current prequels. But, if you watched them 1-6 sequentially, the big shock of Vader's true identity would remain intact, which is something the current prequels don't accomplish.

Wanting to find a way to preserve that is, in fact, what initially compelled me to develop the alternate storyline.