http://en.wikipedia.org/wiki/Irish_name

First or given names

The Irish have a traditional system for naming children [citation needed] : the first son is named after the father's father, the second son after the mother's father, the third son after the father, the first daughter after the mother's mother, the second daughter after the father's mother, the third daughter after the mother. Any further children are named by the parents' choice. This has led to some spectacular names being made more common, for example there are plenty of Assumptas and Perpetuas, and many girls were named after Saints Theresa and Bernadette in the 1950s shortly after they were canonised. Many families still adhere to this way of naming children, although it is becoming less common nowadays with the influx of more secular names from the world of TV and popular music [citation needed]. Traditional names, like Gráinne, Áine and Cathal, or Irish versions of Norman names, such as Seán (from Norman French Jean), Siobhán and Sinéad, are also very common. It's possible for several cousins to have exactly the same name, eg. Daniel Murphy, if all their fathers were brothers, and they are named after the same grandfather. To avoid confusion a pet name may be used, or a middle name eg Daniel Patrick may be called Dan Pat, and Daniel John may be called Danny John. Though it has been seen in older high class families [citation needed] were family records are present that the child's name can be that of an ancestors or famous person, such thing is most prominent in the isolated families, such as the Mac Diamadas of Limerick and the Mac Gillachs of Donegal whose families have dated back to the 10th century.

helpful suggestions for Irish research:
 
http://allaboutirish.com/library/gen/dir-gene.shtm