In Greek and Roman mythology, Cycnus or Cygnus (Ancient Greek Κύκνος, "swan") is king of the Ligurians, kinsman and beloved of Phaethon. Mourning Phaethon among the poplars on the Eridanus, he is transformed into a swan that shuns the sky and keeps to lakes and rivers. Distinct from Cycnus son of Ares, Cycnus son of Poseidon slain by Achilles, and Apollo's Tempe beloved of the same name.
Adapted from Wikipedia, "Cycnus" · CC BY-SA 4.0
I.Phaethon's mourner
Ovid's Metamorphoses makes Cycnus son of Sthenelus, ruler of Ligurian peoples, related to Phaethon through his mother and joined to him in love. Leaving throne and cities, he laments on the green banks of the Eridanus where the Heliades stand as weeping trees. Grief thins his voice to song; white plumage covers him; a long neck stretches out — he becomes a swan that distrusts the heavens and Jove's fire and seeks still waters, enemy of flame.
Hyginus Fabulae 154 belongs to the same Phaethon cluster. The Ligurian king is the Cycnus of the Eridanus swan, not a Trojan War antagonist.
II.Homonyms
Wikipedia's Cycnus page catalogues several swan-heroes: son of Ares killed by Heracles; son of Poseidon killed by Achilles; Apollo's boy at Tempe; and this Ligurian friend of Phaethon. The atlas id cycnus-liguria is only the Ligurian king of Ovid and Hyginus.