Like 50% of curent Island population they are a come-over family - though pretty far back appearing in the earliest written records !
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].

Thus a well established name both on Island and also in West Lancashire (Liverpool + Fylde area)