Why did Sauron make this claim?

Question

When he found how greatly his knowledge was admired by all other rational creatures and how easy it was to influence them, his pride became boundless. By the end of the Second Age he assumed the position of Morgoth's representative. By the end of the Third Age (though actually much weaker than before) he claimed to be Morgoth returned.

_{-Letter 183}

It seems an odd thing to claim considering many of the old-school Elves, the Istari and well-learned Men would surely know Morgoth is no more, so why does Sauron claim to be Morgoth? Or is there more to him just saying he is Morgoth?

Answer 1

There are two factors:

1. Presenting an alternate deity-like figure is an effective way to meet his goals
2. He's starting to lose it a bit

The crucial part is earlier in the letter:

[Sauron] had gone the way of all tyrants: beginning well, at least on the level that while desiring to order all things according to his own wisdom he still at first considered the (economic) well-being of other inhabitants of the Earth. But he went further than human tyrants in pride and the lust for domination, being in origin an immortal (angelic) spirit. [...] Sauron desired to be a God-King, and was held to be this by his servants; if he had been victorious he would have demanded divine honour from all rational creatures and absolute temporal power over the whole world.

^{The Letters of J.R.R. Tolkien 183: Notes on W.H. Auden's review of The Return of the King. 1956}

Sauron almost certainly didn't believe he was really Morgoth; in any case, Tolkien says in other writings that he was a professed atheist, but not a true (non-)believer:

Sauron was not a 'sincere' atheist, but he preached atheism, because it weakened resistance to himself (and he had ceased to fear God's action in Arda). [...] To wean one of the God-fearing from their allegiance it is best to propound another unseen object of allegiance and another hope of benefits; propound to him a Lord who will sanction what he desires and not forbid it. Sauron, apparently a defeated rival for world-power, now a mere hostage, can hardly propound himself; but as the former servant and disciple of Melkor, the worship of Melkor will raise him from hostage to high priest.

^{History of Middle-earth X Morgoth's Ring Part 5: "Myths Transformed" Chapter VII: "Notes on motives in the Silmarillion" (i)}

Tolkien is writing this from the perspective of Sauron's time as a prisoner in Númenor, where he wanted to corrupt the Eru-fearing population; presenting an alternative deity is the best way to do that, and Melkor is the best choice - Sauron himself is hardly in a position of power.

After his "escape", though, it's a different story; Sauron suddenly is in a position of power (more so in the Third Age, when he was presumed destroyed and then returned - that's some serious God-cred), so why wouldn't he set himself up as a God-figure?

The specific choice of impersonating Morgoth is, so far as I know, never explored in any writings other than Letter 183, so a word-of-Eru answer is hard to come by; it does, however, present a certain logical sense. Morgoth is still a well-known and well-feared entity in Middle-earth, and most likely even more so in Harad and the East, where Morgoth dominated at least some of the population. It just makes sense.

Answer 2

It seems an odd thing to claim considering many of the old-school Elves, the Istari and well-learned Men would surely know Morgoth is no more...

And they did. The problem, though, is that they are greatly outnumbered by the realms of Men to the East and South that hold Sauron as their overlord and/or god.

The War of the Ring was going to be lost due to their overwhelming numbers, not by (direct) intervention by Sauron as a semi-divine being. From a strategic standpoint, Sauron did not care what the remnants of the Noldor and Númenóreans knew or believed, because it didn't affect his true power base.

However, the realms of the East and South were only united directly against the West due to the influence and will of Sauron. When that was destroyed along with the Ring, his former subjects either surrendered or fled. That's why, even if the Ring had not been destroyed, Sauron would have won whether or not he actually recovered the Ring.