Moore (in Manx Surnames online at MNB) has
CORJEAG (pronounced CORJATG), is an attempt at translating the English CAVENDISH, (imagined to mean 'giving dish'!)

'CURJAIG, s.f. an alms dish . . . This word is used for the surname of Cavendish, (in Manks) but more probably giving dish.'*

At the end of the 16th century a family called Cavendish settled in the parish of Michael, where they held property in 1583 (vide Liber Vastarum), and from 1611 (when the Register commences) to 1650 their births, marriages and deaths are duly entered under that name, but after that time, though the family is known not to have died out, the name disappears, and CORJEAG entirely supplants it, the two names having co-existed since 1611. CORJEAGE is still almost confined to Michael, occurring rarely in the adjacent parishes and not at all elsewhere.

Creggen states (early 19th C) that Manx J always pronounced as soft g (gee-gee) in english