Wordorigins.org

Jersey is the largest of the Channel Islands and has lent its name to a US state. The name Jersey, or Gersoi or Jersoi can be traced back to c.1025. It means island of a man named Geirr or *Gērr. It follows an Old Scandinavian topographic naming convention of personal name + -ey.

The name of the US state goes back to one of the original two grant holders of the territory that would become the colony and state, John Berkeley (1602-1678) and George Carteret (1610-1680). Carteret was a native of Jersey and named the territory for his home island.

The word for the sports tunic also comes from the Channel Island. Jersey cloth or jersey-worsted wool was originally a reference to machine-knitted fabric made on the island and then more generally made anywhere. Philip Stubbes’s 1583 The Anatomie of Abuses:

Nether-stocks...not of cloth...for that is thought to base, but of Iarnsey worsted.

(Sources: Oxford English Dictionary, 2nd Edition; Illustrated Dictionary of Place Names; Oxford Dictionary of British Place Names)