Leucippus was the name of many mythological characters. Probably the two best known are the son of Perieres and Gorgophone who became joint king of Messenia with his brother Aphareus, and the son of Oenomaüs who dressed as a girl to win the friendship of Daphne (but who was exposed, in more senses than one, when her companions stripped him to make him swim with them).
This is thus one of the several 'noble' propitious names, 'white horse', meaning someone who could have fine white horses for racing and the like. (Such names have their parallels several thousand miles away in the names of American (Red) Indian chiefs. There must have been more than one 'Big Chief White Horse'.)