This is a matter in dispute among philologists, and I am no authority.
Some say that Caesar meant the Isle of Man when he spoke of Mona; others
say he meant Anglesea. The present name is modern. So is Elian Vannin,
its Manx equivalent. In the Icelandic Sagas the island is called Mon.
Elsewhere it is called Eubonia. One historian thinks the island derives
its name from Mannin--in being an old Celtic word for island, therefore
Meadhon-in (pronounced Mannin) would signify: The middle island. That
definition requires that the Manxman had no hand in naming Man. He would
never think of describing its geographical situation on the sea.
Manxmen say the island got its name from a mythical personage called
Mannanan-Beg-Mac-y-Learr, Little Mannanan, son of Learr. This man was
a sort of Prospero, a magician, and the island's first ruler. The story
goes that if he dreaded an enemy he would enshroud the island in mist,
"and that by art magic." Happy island, where such faith could ever
exist! Modern science knows that mist, and where it comes from.