The name of the flower is universal; it is viola in Latin, vas in Sanscrit; and in Greek anciently Γιον, but afterwards ἴον, whence later Greeks supposed it to have been named from having formed a garland round the head of Ion, the father of the Ionians.
... Whether Viola has ever been a real Italian name I cannot learn, or whether it is only part of the stage property endeared to us by Shakespeare... (History of Christian Names, Yonge, 1884)

    Twelfth Night, a drama by Shakespeare.  The story came originally from a novelletti by Bandello (who died 1555), reproduced by Belleforest in his Histoires Tragiques, from which Shakespeare obtained his story.  The tale is this:  Viola and Sebastien were twins, and exactly alike.  When grown up, they were ship-wrecked off the coast of Illyria, and both were saved.  Viola, being separated from her brother, in order to obtain a livelihood, dressed like her brother and took the situation of page under the duke Orsino.  The duke, at the time, happened to be in love with Olivia, and as the lady looked coldly on his suit, he sent Viola to advance it, but the wilful Olivia, instead of melting towards the duke, fell in love with his beautiful page.  One day, Sebastien, the twin-brother of Viola, being attacked in a street brawl before Olivia's house, the lady, thinking him to be the page, invited him in, and they soon grew to such familiar terms that they agreed to become man and wife.  About the same time, the duke discovered his page to be a most beautiful woman, and, as he could not marry his first love, he made Viola his wife and the duchess of Illyria. (Reader's Handbook of Famous Names in Fiction, etc., Brewer, v.2, 1899)