Goddesses of the Moon in Greek Myths

Euryunome

In ancient Greek mythology, an astonishing beam of light emerged from chaos, and it was the Goddess of the Moon (probably the most ancient one in history), Euryunome (also mean traveler to far beyond). Her dancing footsteps separate the sky from the sea, then she was surrounded by wind from all direction, which was captured by Ophion (serpent of the moon, or egg of the universe) She transformed into a white bird, creating a nest in the sky. In the nest, she laid silver eggs, which became the sun, moon and stars.
Above legend can be founded in some versions of Greek Legend, where Euryunome and the serpent Ophion had been ruler of the world.
In Greek Mythology, Euryunome was the daughter of Oceanus (God of Ocean, Titans, son of Uranus and Gaia) and Tethys (Titaness, aquatic sea goddess). She ruled Mount Olympus together with Ophion.
After Kronos's domination of Mount Olympus
Afterwards, Rhea and Cronus defeated Euryunome and Ophion, who fell into the deepest of the underworld. There had been legends they had fled to other mountains, to the sea, or being killed, and there was no unified opinion yet.

Theia

Theia is the mother of Helios, the God of the Sun. Theia has the meaning of Daughter of God, and God of the moon. Childern of Theia and Hyperion (another major God in older Greek myths) cosnsits of Helios (represent the sun), Selene (represent the moon) and Eos (Goddess of Dawn), which become important in later legends about origin of ancestors of Greeks.

Hecate

Hecate is another goddess in Greek myths associated with the moon. She is the daughter of Asteria and Persēs. Asteria later become the island where Apollōn and Artemis are born. Persēs is sister of Europa and previously mentioned Euryunome (Some clever ones may realised that both parents of Hecate are female, we don't know whether it was a mistake of the ancient writers or anything else, anyway, there is no way to find evidance)
In fact, Hecate is Goddess of full moon and the night, and usually the ancient authors or poets would confuse it with another two famous Lunar Goddess Selsne and Artemis. Hecate is also the Guardian god of crossroads and Three-forked roads. According to the myths, she had three different bodies, as a female Hound, as a female horse, and as a female wolf, while she can transfer to any one of them. In ancient Greece, there had been some ceremonies worshiping Hecate during the night of full moon.
Hecate is also be regarded to be Goddess of vengeance and related to revenge. It is said to be widely worshiped by witches during middle ages of Europe.
By the way, she is also said to be the origin samba God Hekato of ancient Egypt.

Selene

Before Artemis is widely worshiped as Lunar Goddess, Selene has already been describled in many stories and legends. Selene is related to the God of light - Sera, and it appeared to be its alternative appearance, with the female image of Lunar or the Moon. Selene is widely regarded as Goddess of Moon around Asia Minor.

Artemis

Symbolising crescent moon, Artemis is one of the most widely worshiped Goddess of Moon in many ancient cultures. Artemis is not from Greek legends, she is probably from religious beliefs in Asia Minor, though there is no obvious evidence of where she is from. Artemus is also said to be younger sister of Apollōn.

Europa (Europe)

Europa is the goddess of the moon that are relevant to the bull. Son of Zeus and Europa is Minos, who later become King of Crete. According to Greek legend, kings of Minos dynasty would marry with Goddess of Moon, Minotaus - the Guardian in the labyrinth, will reincarnate whenever a new king is founded.