Moore see http://www.ee.surrey.ac.uk/Contrib/manx/manxnb/v05p020.htmhas
MOORE [1499], MORE [1511].

MORE is the usual form till the end of the 16th Century. It is a common name in Ireland, Scotland, and the North of England, as well as in the Isle of Mann.

found in:
Braddan, Santon, Malew, Arbory (very common), Ballaugh, Marown, Maughold, German, Bride, Rushen, Lorian, Patrick, Onchan (c), Michael, Andreas, Jurby (u).

three Moore families are covered in 'Old Manx families
see http://www.ee.surrey.ac.uk/Contrib/manx/famhist/families/awm1889/moore_a.htm and then links from this

Many manx records are on Mormon microfilm - daytrips to Douglas only 32pounds from Liverpool on the Cat - the manx museum is half mile walk from sea terminal