Mythology

...Moon - Serenity - Selene...

The first one is because Serenity falls in love with Endymion so it leads us to the Greek myth of the moon goddess Selene.

Apollonius of Rhodes refers to Selene, "daughter of Titan", who "madly" loved a mortal, the handsome hunter or shepherd—or, in the version Pausanias knew, a king— of Elis, named Endymion, from Asia Minor.
- Wikipedia

The second thing is that on the moon there is the sea of Serenity or known as Mare Serenitatis, where in the story is located the first Moon Kingdom of the past

Mare Serenitatis (the "Sea of Serenity") is a lunar mare that sits just to the east of Mare Imbrium on the Moon.
- Wikipedia

...Rabbit of the Moon

This one is based on a Japanese myth, because if we translate Tsukino Usagi we find out that it’s the rabbit of the moon, some word-games that Naoko-sensei enjoys.

The Moon rabbit, also called the Jade Rabbit, is a rabbit that lives on the moon in East Asian folklore. The legends about the moon rabbit are based on the traditional pareidolia that identifies the markings of the moon as a rabbit pounding in a mortar. In Chinese folklore, it is often portrayed as a companion of the moon goddess Chang'e, constantly pounding the elixir of life for her; but in Japanese and Korean versions it is just pounding mochi or tteok.
- Wikipedia