you say
Her parents were Philip COTTEEN and Margaret SANTON
have you examined actual register - all the cases I've seen where a family name equalled a place name on the Island (other than the name Douglas) was a misreading of the register where an out of parish spouse was indicated as such (eg in Andreas where I have looked at the first 90 years of register the IGI has included one 'Lezayre' one 'Ramsey' a couple of 'Smeale's etc