Yes, the genitive or 'possessive' case, its a grammatical term. Without a rudimentary knowledge of grammar its very difficult to discuss the way a language works.

In the Irish tradition a woman who married could be referred to as 'the woman of X', but might continue to use her own name as 'the daughter of Y'. This custom was not specific to any district of Ireland but as the new English language and customs superseded the old, spreading from the east toward the west, it is now seen as a Gaeltacht thing.