All species of Eurybia were previously been treated as members of the Aster genus in North American floras. The new nomenclature is strongly supported on the basis of morphology because the species of North America are not genetically related to members of the Eurasian genus Aster.
In Greek mythology, Eurybia was married to the titan Crius and gave birth to three known offsprings Astraios, Perses, and Pallas. She was a minor sea goddess under the dominion of Poseidon. Her parents were Pontos and Gaia. To be married to a titan you have to be very strong, powerful, which might again qualify the genus.
In Greek mythology, Eurybia was also one of Thespius's daughter. Thespius was a legendary king of Thespiae, Boeotia. He was reportedly son of Erechtheus, King of Athens and Praxithea. His maternal grandparents were Phrasimus and Diogenia. Diogenia was daughter of the river god Cephissus. He married Megamede, daughter of Arneus. They reportedly had fifty daughters together. Though Thespius may have fathered some of the daughters from unnamed mistresses with Megamede being their stepmother.
All his daughters came of marrying age but Thespius seems to have sought no husband for them. He instead desired grandchildren from the hero Heracles. When Heracles was assigned to kill a lion (not to be confused with the Nemean Lion), Thespius offered his fifty daughters as a prize. The hunt for the lion lasted fifty days, and during each night of the hunt Heracles slept with each of the fifty daughters, who in turn each gave birth to one son. Alternate sources claim that Heracles slept with the daughters in a single night. In this version, only forty-nine slept with the hero, with the fiftieth being destined to serve as a virgin priestess in a temple to Herakles. In this version there were fifty-one grandsons of Thespius, of which forty colonized the island of Sardinia. The daughters are often referred to as the Thespiades. As for Eurybia, one of the fifty daughters, she was the mother of Polylaus. And being, even for a single night, the wife of Heracles, you had to be very strong, powerful, which might again qualify the genus. (The daughters of Thespius were the subject of a 1853 painting by Gustave Moreau).