1. Proserpine (Persephone to the Greeks)
    This is my number one: She inhabits the underworld which fits a body so deep in the dark. Proserpine was stolen into the underworld and there is some thought that Planet Nine was kicked into the outer solar system early in its formation. She is often associated with the coming forth and withdrawal of seasons which has a nice symmetry with Planet Nine's supposed highly eccentric orbit. And it would be a nice nod to poor Pluto, husband to Proserpine. Downside: kind of a ugly name.
  2. Latona (Leto to the Greeks)
    Mistress to Jupiter, she hid herself away to avoid the wrath of his wife Juno, who demanded that everyone shun her. She is also the mother of Apollo the sun, to whom Planet Nine is still bound despite her exile.
  3. Juno (Hera to the Greeks)
    Fitting because she is wife to Jupiter and mother to almost everybody else. He rules in size but she cradles the whole solar system in her orbital bosom. Also she is jealous of Venus who has the glory of the sun. Finally it's a nice sounding and memorable name.
  4. Diana (Artemis to the Greeks)
    Mostly because I love Artemis but also: She is associated with the moon and by extension the night, fitting for a planet in perpetual darkness. She is sister to Apollo, the sun, which is also fitting. Finally, she eschewed the company of men, just as Planet Nine keeps herself apart from the boys of the solar system. Downside: It is also an ordinary English name which makes it a little boring.