Why do the main characters take their names Prometheus and Gaea? Why weren't they allowed to choose their names in their old society?

Equality decides that they must choose their own names that distinguish them from others as names used to do in the Unmentionable Times. He chooses Prometheus, after the ancient man who brought light from god to man and was punished for his kindness. For the Golden One, he chooses Gaea, after the earth goddess who was the mother of all other gods.

Prometheus' ceremonial changing of names is a natural corollary to his celebration of "ego," the word that ends his narrative. By discarding their assigned names, they engage in a final rejection of collectivism and of the numerical designations that made each man a disposable part rather than a viable individual. By ridding himself of the misuse of Equality in his name, the protagonist makes a statement against the idea of compulsory equality, where equality means slavery and forcibly making everyone average rather than simply allowing to men to reach their full potential without legal restrictions. Liberty 5-3000, meanwhile, changes her name to Gaea and thus causes the idea of liberty to lose its ironic meaning. Additionally, by dispensing with the appellation "the Golden One," she shows that they do not need to describe her individual characteristics to establish her overall individuality.