The Mouth of Sauron

[Balin999]

I am under the impression that the lines of the Ring Verse, except the line on the Ring itself, were the creations of the elves after the fact, not actually said by Sauron.

I did a bit of research on this subject. Here are two quotes I found:

One Ring,... "It is only two lines of a verse long known in Elven-lore" (Gandalf, The Shadow of the Past)

Why should the Elves cite Sauron? Did they know that Sauron said that, and made the whole verse out of it?

For in the day that Sauron first put on the One, Celebrimbor, maker of the Three (!), was aware of him, and from afar he heard him speak these words, and so his evil purposes were revealed. (Gandalf, Council of Elrond)

Hm, it doesn't say at all if Sauron spoke the whole stuff or just the two lines.

And the Nazgul's bodies didn't rot away: they faded into the wraith world, still being existent as was Frodo's when he wore the Ring.

Well, ok, my fault, but at least they were not visible for mortals any more.

Tolkien applies the characteristic of unity to the dark forces and the characteristic of diversity to the people of the west.

Think of the orcs. There was not only one race, there were many of them. Uruks, the small ones of Moria, and the long armed Mordor-Orcs.
I think they were only so similar because the good ones simply didn't know much of them and so couldn't distinguish between them.
A quote comes to my mind. "To sheep other sheep may appear different."
And they had different banners and all that, so I guess there were some differences among the races under Saurons control.
But you are right with your thoughts regarding the Mouth. Of course it is out of the question for him to have a name, BUT: he once had one, he had only forgotten it.
Nevertheless I think your theory could be right.