The story
Possibly of Old Norse origin, from Ǫngullsey (“hook island”) (ǫngull + ey) or Ǫnglisey (“Ǫngli's island”), the name Ǫngli itself being a variant of Ǫngull and from the former noun. Folk etymology confused the name with that of the Angles. More at Anglesey.
Etymology from Wiktionary, CC BY-SA 4.0.