I had the same question some time ago. The Wikipedia page is, as always, quite interesting. Although I think the tl;dr is "the name's so old, no one really knows". But the theory is:
"The name is probably cognate with the Welsh name of the island of Anglesey, Ynys Môn, usually derived from a Celtic word for 'mountain' (reflected in Welsh mynydd, Breton menez, and Scottish Gaelic monadh), from a Proto-Celtic *moniyos."
https://en.wikipedia.org/wiki/Isle_of_Man#Name
"The name is probably cognate with the Welsh name of the island of Anglesey, Ynys Môn, usually derived from a Celtic word for 'mountain' (reflected in Welsh mynydd, Breton menez, and Scottish Gaelic monadh), from a Proto-Celtic *moniyos."