@pyan Correct. The bells of Rivendell are ringing for you!
Here's my explanation of the rhyme.... I was looking for Aragorn and Turin.
Fostered by Elves and born in the North, Only Aragorn, Turin, and Tuor are recorded as fostered by Elves after being born in the north
To guard the land, I was sent forth. Turin served with the march wardens of Doriath, Aragron was a ranger
My famous sword was known as well;
It began with an A and ended in L. The only three swords that fit are Andruril (Aragorn), Anguirel (Eol, Thingol), and Anglachel (Eol, Thingol, Mablung, Turin)
My friends were glad and my foes knew dread
when seeing an object on my head. Turin bore the dragon helm of Dor-lomin and Aragorn the Elessar, the Elfstone of Earendil
I did not requite a royal maid's affection, Finduilas (Turin) and Eowyn (Aragorn)
but learned of an augury in her direction. Glaurung prophesied that Finduilas was Turin's only escape from his doom. Aragorn knew that "no living man" could defeat the Witch-king.
Of my names, one's akin to an Elf; Adanedhel or Elf-man for Turin. Elessar or Elf-stone for Aragorn
but the most acclaimed I gave myself. Turin called himself Turambar. Aragorn named himself Telcontar which became the dynastic name of all future kings of both Arnor and Gondor.
Family pride was one of my goals. Turin tried to live up to Hurin, Galdor, Hador and Marach. Aragorn was conscious of his ancestor's successes and failures... Arvedui, Isildur, Elendil, Elros, Earendil, Beren
My sire's renowned fight was 'gainst the Trolls. Hurin's greatest fight was the rear guard action to cover Turgon's retreat in the Nirnaeth Arnoediad. After the deaths of Fingon and Huor, Hurin fought against the Troll body guard of Gothmog. Arathorn's only recorded fight, as far as I know, was the one in which he died fighting Trolls.