Who declared the Last Alliance to be the "last" and why?

Question

Who named it, why and when? Some possibilities I can think of:

• They themselves chose it, meaning that if they would overthrow and destroy Sauron, no more such alliances would be needed.

• Someone gave the name in retrospect (Elrond?, Isildur?) deeming that the great losses of the Eldar prevented them from ever again fielding a comparable force. This seems the most commonly accepted version. But someone writing right after the fall of Nargothrond could easily have declared the League of Maedhros to have been a "Last Alliance of Elves and Men" too.

• It was originally intended as "the most recent alliance", without capitals, and only later had folks understood it to mean "final alliance"

• The name somehow originates from Sauron, who spread it by agents to suggest the impression to the Dúnedain that they can no longer count on elven assistance.

Answer 1

Elendil and Gil-galad named it as such. Had they not defeated Sauron, they would literally have been the last alliance.

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The Last Alliance of Elves and Men was indeed so great that it is noted to be only shadowed by the host of the Valar, which was assembled near the end of the First Age to overthrow Morgoth.

Now Elendil and Gil-galad took counsel together, for they perceived that Sauron would grow too strong and would overcome all his enemies one by one, if they did not unite against him. Therefore they made that League which is called the Last Alliance, and they marched east into Middle-earth gathering a great host of Elves and Men; and they halted for a while at Imdralis. It is said that the host that was there assembled was fairer and more splendid in arms than any has since been seen in Middle-earth, and none greater has been mustered since the host of the Valar went against Thangorodrim.

_{The Silmarillion, "Of the Rings of Power and the Third Age"}

So yes, the Last Alliance was mightier a host than any other after the final one the Valar raised against Morgoth. Even greater than anything the Númenóreans sent against Sauron throughout the Second Age.

The battle was so instrumental for the inhabitants of Middle-earth that nearly every living thing played a role, at least, in the battle. The text here is a little silly in suggesting that Orcs fought Orcs on both sides. But based on prerequisite knowledge, I think it's safe to safe that the Orcs did not fight on the side of the Elves.

All living things were divided in that day, and some of every kind, even of beasts and birds, were found in either host, save the Elves only.

_{The Silmarillion, "Of the Rings of Power and the Third Age"}

And rightly so, because if they had not stopped Sauron there and then, with the Ruling Ring he would have laid dominion over Middle-earth. Sauron had been amassing his forces for many years ever since his escape from Númenor, and his forces not only comprised of Orcs then but also the Haradrim at that time, and countless others.

One thing different about this war and that of the First Age, is that Men play a larger role. Or at least, the Númenóreans in particular. Remember that Sauron was the catalyst that caused the downfall of Númenor, and their enemy. Perhaps also because Middle-earth is now smaller, but the proportion of Men to Elves has increased since the First Age. That is why Maedhros' army wouldn't be called that of Elves and Men, because really, the Elves then seemed to be the leaders more so than the Men (the minority). But in the Second Age, things would have been different thanks to the large population of Númenóreans, and fewer Elves than before.

The leaving of the Noldor probably also played a role in the naming of the "Last" Alliance. Already, since the end of the First Age, the Noldor had begun returning to Valinor, and would do so throughout the Ages that came after. With the dwindling of such "High Elves", it's unlikely Middle-earth would ever see such a great host as that comprised of the Noldor Elves.

I do not think that they believed that evil would have been vanquished forever that no other such alliances would have been needed. They would at least rid Middle-earth of Sauron (for a time), but ultimately what evils come afterwards will have to be dealt with. As Gandalf says,

Yet it is not our part to master all the tides of the world, but to do what is in us for the succour of those years wherein we are set, uprooting the evil in the fields that we know, so that those who live after may have clean earth to till. What weather they shall have is not ours to rule.

That brings us back to the conclusion that the leaders of the alliance, Elendil and Gil-galad, indeed named it as such in retrospect that, had they not defeated Sauron then, they would not have ever be able to muster another army of that size, power and majesty again.

Answer 2

The trend throughout the Second Age clearly showed the decline of the Eldar (mainly the Noldor) and the rise of Men. Indeed, Gil-galad recognized this early on, in a letter to Tar-Meneldur in S.A. 883:

A new shadow arises in the East. It is no tyranny of evil Men, as your son believes; but a servant of Morgoth is stirring, and evil things wake again. Each year it gains in strength, for most Men are ripe to its purpose. Not far off is the day, I judge, when it will become too great for the Eldar unaided to withstand. Therefore, whenever I behold a tall ship of the Kings of Men, my heart is eased. And now I make bold to seek your help. If you have any strength of Men to spare, lend it to me, I beg.

Unfinished Tales, Part 2.II, "Aldarion and Erendis"

(To this point, Númenor had minimal dealings with Middle-earth; indeed, there as no contact at all until 600. Tar-Meneldur stepped down and passed the throne to his son Aldarion—who had been providing council and aid to Gil-galad for some years prior—rather than make the decision to involve Númenor in the affairs of Middle-earth himself.)

Centuries later, after the creation of the One Ring triggered war between Sauron and the Noldor, Sauron was able to occupy all of Eriador between 1695 and 1700, with the Noldor holding on only to Lindon in the extreme west until the arrival of a Númenórean fleet in 1700 turned the tide.

By the end of the Second Age, both races realized that this would be the last time that Men and Elves would stand together as equals, as the Noldor continued to decline both in numbers and in "vitality". Win or lose, I suspect many of the Noldor had decided it was time to depart Middle-earth as so many of their kin had decided to do at the beginning of the Age.