Rainbow is a Hippocampus that was named by Tyson in the Sea of Monsters. He appears in the second and final book, and in the second movie. He's a half horse and half fish creature.
Percy Jackson and the Olympians
The Sea of Monsters
Rainbow is half-horse, half-fish, or a Hippocampus ("Fish Ponies" as Tyson calls them). Rainbow appears with two other hippocampi at the beginning of the quest, as a gift from Percy's father, Poseidon. They take Tyson, Annabeth Chase, and Percy Jackson to the Princess Andromeda, Luke Castellan's ship. Rainbow is sad to leave his new friend, and performs backflips with Tyson on his back trying to get him to stay. When that doesn't work he follows them to the Sea of Monsters, and rescues Tyson from the ship, CSS Birmingham when it explodes. He takes Tyson and searches the sea for Percy and Annabeth, finally finding them at Polyphemus' Island. Shortly after he rescues Percy and his companions, with the help of his fellow Hippocampi when Blackbeard's ship, Queen Anne's Revenge, sinks and takes them to Miami, where the Hippocampi start sneezing and feeling sick, because of all the pollution. After the quest, Tyson rides him to the Cyclopes forges.