I was able to find the reference to all peoples and beasts during the Last Alliance:
Quote:
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From Imladris they crossed the Misty Mountains by many passes and marched down the River Anduin, and so came at last upon the host of Sauron on Dagorlad, the Battle Plain, which lies before the gate of the Black Land. 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. They alone were undivided and followed Gil-galad. Of the Dwarves few fought upon either side; but the kindred of Durin of Moria fought against Sauron.~Of the Rings of Power and the Third Age
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It could be Tolkien writing poetically when saying "All living things were divided in that day," but I think it's fair to say that yes the "Last Alliance of Elves and Men" is a misnomer, and only the Elves were undivided.
Editting because I don't want to triple post, but a few more quick things came to mind from finding the reference in
Of The Rings of Power:
-The Elves were undivided, so they must have been the largest force at the Battle of Dagorlad. We know that Cirdan was present, Elrond was Gil-galad's 2nd in command, Amdir and Oropher had armies. Oropher unwilling to completely submit to Gil-galad's command hastily led an attack and the Silvan elves he led took the heaviest casualties.
-I would say Men likely made up more than dwarves, since Of the Rings of Power says "few dwarves fought upon either side." I'm not sure if it's known what other commanders of Men would be present, besides Elendil, Isildur, and Anarion. I would guess Isildur and Anarion led different forces from Elendil's. Isildur was the one who cursed the Men of Dunharrow when he summoned them to their oath, but they reneged.