The name is usually segmented Eury-nome, where eury- is "wide". This segment appears in Linear B as e-u-ru–, a prefix in a few men’s names. It does not occur in any Mycenaean women’s names, nor does –nome. The root of –nome is Proto-Indo-European *nem-, distribute, as in the Greek infinitive, nemein, "to distribute." Words derived from *nem- had a large variety of senses. In the case of Eurynome, the two main senses proposed are "wanderer" and "ruler". Robert Gravessaw in Eurynome a lunar goddess descending from the Pre-Hellenic mother goddess of Neolithic Europe. In that case, –nome is as in our word nomad. The nomad wanders searching for pastureland, or land that has been "distributed" for the use of domestic animals. The moon is to be regarded as wandering. In the other interpretation, –nome is as in English auto-nomy. A ruler is someone who "distributes" law and justice. Neither case has any bearing on the status of Eurynome as a possible Pelasgian mother goddess. If Eurynome was the descendant of a pre-Greek goddess, she must have had a pre-Greek name, and not the Greek name, Eurynome. If the name is Indo-European, it might have evolved into Greek with the rest of the language. If it is not Indo-European, then it might result from renaming or from selecting the closest Greek homonym.
Mythology
In the epic tradition, Eurynome was one of the elder Oceanides, that is, a daughter of Oceanus and Tethys. Eurynome was the third bride of Zeus and mother of the Charites, goddesses of grace and beauty. When Hephaestus was cast from Olympus by the goddessHera, who was disgusted at having borne a crippled child, he was caught by Eurynome and Thetis. Eurynome and Thetis nursed the god Hephaestus on the banks of the earth-encircling river Oceanus, after his fall from heaven. Charis, Eurynome's daughter, later became Hephaestus' bride. Eurynome is closely identified with another Eurynome, Queen of the Titans. This Eurynome was an early Titan queen who ruled Olympus beside her husband Ophion. The pair were wrestled for their thrones by Cronus and Rhea who cast them down into the earth-encircling river Oceanus.
Homer's account
18.388ff
Hesiod's account
Homer and Hesiod establish that a belief in the Oceanid existed in the earliest literary times. The most likely circumstance, based on the testimony of Pausanias, is that both authors took their themes from a religion known to and believed in by all the Hellenes; thus, it is probably best to assume that Eurynome the Oceanid is the same Oceanid of ancient Greek belief mentioned in all the classical sources.
Pausanias' account
8.41.5, 6 9.35.5
Apollodorus' account
Worship
Eurynome was worshipped at the confluence of the rivers Neda and Lymax in Arcadia. Her xoanon, which could only be viewed when her sanctuary was opened once a year, was a wooden statue bound in golden chains depicting a woman's upper body and the lower body of a fish. Her son Asopus was the god of a nearby stream in the adjacent region of Sikyonia. The fish-tailed goddess, Eurynome, worshipped in Arcadia, may have been Eurynome wife of Ophion, Tethys the wife of Oceanus, Eurynome mother of the Charites, the goddess of the river Neda, or a watery Artemis.