The Manx Norris's came from Lancashire
(see Moore manx names on Manxnotebook - NORRIS, formerly NORRES (extinct). This family followed the Stanleys from Lancashire to the Isle of Mann, where they held several important official positions.

'Gubon John NORREST [1422], Sir Huan NORREST [1499], NORRIS [1586]

Norris is a quite common name in South West Lancashire - I dpn't know of its derivation - try one of the Lancashire Genealogy boards