How did Viola come to be known as Cesario?

In Twelfth Night, following a storm at sea, the travelers Viola and her twin brother Sebastian find themselves shipwrecked and separated on the coast of Illyria. The ship's captain, who makes land with Viola, thinks Sebastian also survived.
Viola wants to get situated in the new country while looking for her brother, and her first idea is to become a lady-in-waiting to the fine noblewoman Olivia, about whom the captain has been speaking. However, upon hearing that Olivia is in mourning and retreat, Viola concocts a new plan: disguised as a man, she will enter the court of Orsino, the Duke of Illyria, where she will serve him as a eunuch.
The captain gives her some dry men's clothes, and she sets off to activate her plan. Her new identity is Cesario.