[Pitchwife]

I think Zil has some good points. I can quite well imagine Sauron adopting the name he was given out of defiance in his dealings with the West - à la, "They call me The Abhorred? Let them; I'll teach them horror!" (Although this doesn't go quite so well with those other etymologies where Sauron means "foul stench" or something of the like.) And it's also likely that the policy about the use of that name was different in foreign relations and for his own forces.

Originally Posted by Inziladun

I do think it likely he didn't want his own servants to use that name under normal circumstances. He was not only their ruler, but aspired to be their god as well.

Very true, and this in a somewhat perverse way reminds me of the Jewish taboo against using the proper name of God (YHWH). It's not unlikely that Sauron's followers (at least the lower ranks) were under a 'religious' prohibition to utter his name, so that they had to refer to him as The Great Eye, Him, etc. instead, much like the forbidden name YHWH was paraphrased with other names (Elohim, Adonai, Shaddai, The Holy One, The Most High etc.).
As for the use of Sauron by high-ranking servants of the Dark Lord, such as The Mouth or the emissary to Erebor, that's a difficult question. What exactly were their feelings for the master they served? Fear, of course - but aside from that? Did they still believe the propaganda and consider him admirable, or did they know exactly their lord was the Worst Abomination in Middle-earth but just couldn't help going on serving him? I'd think a sort of love-hate relationship (maybe with a good dose of self-loathing in the mixture) most likely; and in this case, it might indeed have given The Mouth a perverse pleasure to call his master by his right name (using diplomatic license as an excuse), although he probably wouldn't have dared to use it within the walls of Barad-dûr.
If only there wasn't that quite apodictic statement by Aragorn, which seems to contradict all that. Obsolete information on Aragorn's part is one possibility, and simple inconsistency on Tolkien's another (though this would be much too easy); But maybe there's a third. From the article I linked to above:

Originally Posted by Helge Fauskanger

In the Adûnaic (Númenorean) tongue, he was apparently known as Zigûr, the Wizard (SD:247, 250, cf. 437).
One Quenya word for “wizard” is sairon (LR:385), and I have actually seen a suggestion to the effect that Sairon was the actual name of this Maia, which his enemies punningly altered to Sauron when he joined Morgoth.

So maybe The Mouth and the other emissary actually used Sairon, and Frodo's witnesses (remember he, the presumed author of the Red Book, wasn't present at either of the occasions) misheard it as Sauron, the name they were familiar with? They could easily have taken the slight difference for dialectal pronunciation...

(One last thought: one of the meanings given for the adjective maira, from which Mairon is derived, is "precious". So at least the part of Sauron he put into the Ring still had the pleasure of being called by its proper name...)

EDIT: This took me forever to write, so I x-ed with PotH and Sarumian.)