Prometheus is the Greek God of ingenuity and progress; Gaea is the Earth goddess whose essence and influence is given to all generations who follow her. In Rand's story, her main character, Equality 7-2521 is one who is interested in science and progress. Prometheus is a name that fits her main character's personality and interests. Rand was not a member of any religion, so she didn't choose Eve for the female's name, but that seems to be an image or story many can relate to in the Christian era. Rand's main female would be the first mother of a new population of people because she and her husband are alone outside of the city limits. They are starting a new civilization, so she would be the first mother, like Eve. But since Rand's main male character gave himself a Greek name that characterized himself, then why not give his wife a Greek goddess's name, too? Of course, the name for her would reflect earth which gives life to all living things, thereby connecting the name to the woman who would give birth to a new generation.
Prometheus, of Greek mythology, was a Titan, the forerunners of the Greek gods, who stole fire from Zeus (who was not a Titan) and gave the fire to mortals. Prometheus was horribly punished for this crime against Zeus and against order. He was also the god of forethought and the molder of humankind from clay. It was his desire to better the existence of humans that led to his conflicts with Zeus.
Gaea (also Gaia) was a Protogenos goddess, one of the original deities connected with the original primeval elements of the universe. Some of these were Earth, Air, Sea, Sky, Fresh Water, Underworld, Darkness, Night, Light, Day, Procreation, and Time. Gaea is the mother of Earth, the begetter of the universe. Her anthropomorphic depiction shows her as being at one with and inseparable from the Earth: her legs remain only partially risen from the ground.
In Anthem, Equality 7-2521, was a scientist unrecognized.
We loved the Science of Things. ... we awoke in the night ... and we thought that we wished to be sent to the Home of the Scholars when our time would come.
All the great modern inventions come from the Home of the Scholars, ...
He is consigned to street sweeping for his life's work; rediscovers electricity, a form of fire; and takes it to the the World Council of Scholars in order to improve the lives of his fellowkind. He is horribly punished for his actions. In this, you can see the parallel to Prometheus as each brings the potent power of the world as a gift to improve life and is then horribly punished. Equality 7-2521 parallels a Titan since he is the first of a new line of free people.
When Equality 7-2521 is working in an isolated area one day he meets Liberty 5-3000, having the mischance of falling in love with her--falling in love is directly forbidden in their land.
It is our second Transgression of Preference, for we do not think of all our brothers, as we must, but only of one, and their name is Liberty 5-3000.
She follows him as he flees his punishment and they resume their forbidden love in the forest. Equality 7-2521 tells her that she shall be the mother of all that is to come. From the books they find in the forest's abandoned house dating from before the Great Rebirth, they choose names for themselves: Prometheus because, like Equality, he was a light bearer and Gaea because she was known as the mother of all that was new, as Liberty would come to be known.
He took the light of the gods and he brought it to men, and he taught men to be gods. And he suffered for his deed as all bearers of light must suffer. His name was Prometheus. And I have read of a goddess who was the mother of the earth and of all the gods. Her name was Gaea. Let this be your name, my Golden One, for you are to be the mother of a new kind of gods.