In ANH when Tarkin says “The Jedi are extinct, their fire has gone out of the universe. You, my friend, are all that’s left of their religion”. This implies that Vader is meant to be a “Dark Jedi” or a Jedi who uses the dark side of the force, so the word Sith shouldn’t be used in the PT.
Things like the Rule of Two were just made up as an explanation for why Vader and Palpatine were the only ones in the OT.
A lot of people assume that, but Vader and Palpatine were always supposed to be called “Sith”, even when the OT was being made: there was a deleted line in ANH’s Imperial council scene where Vader was said to be a “Sith Lord sent by the Emperor”, and the novelization referred to Vader as a “Dark Lord of the Sith” in his very first scene.
When Obi-Wan says to Vader “Only a master of evil Darth” this implies that this is the first part of his name and not a title that was given to him, so all other Sith/Dark Jedi shouldn’t have Darth in their names. Palpatine should just be known as Palpatine, Count Dooku should just be known as Count Dooku, and when the name Darth Vader comes up it shouldn’t be revealed that it’s referring to Anakin.
That was obviously the intention in ANH, but only because they hadn’t come up with the “Anakin became Vader” twist yet: “Darth Vader” was supposed to be his actual name. But once the father twist was written in ESB, Obi-Wan suddenly started saying “Vader” instead of “Darth”, implying that “Darth” was now a title given to Vader once he turned to the dark side.
Overall, I feel like the portrayal of the Sith in the prequels is perfectly consistent with their portrayal in the OT, and I don’t really see the need to radically change it for “consistency” like some editors have done. I’m fine with cutting the Rule of Two though, but only because Disney has pretty much forgotten about it with all the Sith Inquisitors and Sith Acolytes running around.