Eurynome (the Oceanid mother of the Charites) and Thetis with the infant Hephaestus thrown from the Olymp

In Greek mythology, there were many women with the name Eurýnomê ("far ruling").

• The Oceanid, or daughter of Oceanus.
  1. Wife of Ophion (may be the same as the following)
     
  2. Mother of the Charites (may be the same as the following)
     
  3. Daughter of King Nisus of Megara and mother of Bellerophon by Poseidon according to Hesiod's Catalogue 7 and Hyginus 157.
• Mother of Leucothea whom Helios loved, whose father was the Persian Orchamus, as given by Ovid in Metamorphoses 4.208ff.
  
• Wife of Lycurgus of Arcadia and mother of Amphidamas, Epochus, Ancaeus, and Iasus; from Apollodorus 3.9.2.
  
• Daughter of Iphitus and mother of Adrastus of Argos by Talaus, as given by Hyginus 70.
  
• Waiting woman of Penelope in the Odyssey.
  

Source

Eurynome , mother of the Charites

Iliad Book 18

Hephaestus:

At that time,
I would have suffered heartfelt agonies,
if Thetis and Eurynome, daughter
of the Ocean stream, had not taken me
into their hearts.  With those two, for nine years   
I made many lovely things—broaches, 
spiral bracelets, earrings, necklaces—
inside their hollow cave.  The Ocean stream
flowed round me, always with the roar of surf.  
No one else knew, neither god nor mortal man.
But Thetis and Eurynome—the ones
who rescued me—they knew.

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79 Eurynome is an asteroid.