So...the general rule on this project is that each character gets one name, even if Tolkien gave them a bunch of names, with a few key exceptions that make very good sense in the story. Aredhel will be called Aredhel 100% of the time, and never Ar-Feiniel. She'll dress in white and silver, no problem, but the introduction of a new name to tell us that is not really necessary. So, we're leaving that out.
Sauron is the character with the most names invented by Tolkien (he has, like....over twenty). We are certainly going to use some of them - we've already incorporated Mairon and Sauron, and there was some talk about Thû...and obviously we'll need Annatar. But do we need Lugbûrz? Or Gorthaur? We shall see. So, it would seem to me fairly clear that the goal here is not to rename Sauron every time he appears on screen, but rather to stick to a handful of names for him as needed, and (in general) to resist the urge to make up new names for him.
I'm not saying that we can't...I'm saying that there would have to be a very good reason.