Mick wrote:
As for whether Irish or English names are given, that would be the speaker's choice. Is he/she in the habit of calling Katie/Cáitín by the English or Irish name? Is the speaker the sort of person that is more likely to say “Tá mé i Nua Eabhrac” or “Tá mé in New York”?
Mick wrote:
The names Páidín and Dónall are being used like adjectives: Breandán son of Páidín son of Dónall, but instead of saying “son of” you séimhiú them and put the last name into the genitive case.
This is almost correct, but there is no "son" involved. It is only implied by context. The usage applies equally to females.
The genitive of a proper name is expressed by lenition, e.g.,
bean Pháidín "Páidín's wife".
Breandán Pháidín Dhónaill is literally "Dónall's Paddy's Brendan".