all the other records of the family give mcnameer (or similar) - married as McNamur - a common name in North of Island (sometimes rendered as Monier.
(W W Gill suggests: MacGilmere, MacEmere, Ine Mere, Gilmere as a forename, all 1513. Afterwards in various forms, apparently with an article, of which Macnemeer, 1740, is a type ; finally Monier (stressed on ultimate), then obs. in the Island since mid 19th cent. Mac-giolla-meadhair, son of the joyous youth, would be fairly satisfactory as an ante-type for MaeGilmere. But it may be suspected that two distinct names have been confused, of which one may be, in Mx spelling, Mac-y-Meoir, son of the Steward. Cf. the McAmhaoirs in Glen Orchy, formerly stewards to the Buchanans, and the Mac-an-Mhaoir family who had charge of the Book of Armagh at Ballymoyer.)

Did you check the actual Andreas register as the film is actually of a transcript of that register