I just wondered the same thing and googled an answer which three knoledgeable Irish researchers confirmed saying the exceptions prove the rule. I will bet in different counties things were done in diferent ways.

Irish Naming Patterns for Children:
The 1st son was usually named after the father's father
The 2nd son was usually named after the mother's father
The 3rd son was usually named after the father
The 4th son was usually named after the father's eldest brother
The 5th son was usually named after the mother's eldest brother
The 1st daughter was usually named after the mother's mother
The 2nd daughter was usually named after the father's mother
The 3rd daughter was usually named after the mother
The 4th daughter was usually named after the mother's eldest sister
The 5th daughter was usually named after the father's eldest sister
FROM A GOOGLE SEARCH done 2/13/07
And then somewhere else I read that the first daughter of the second wife was named for the first wife, both names. I never ran that past anybody and I am not sure if both names meant first and middle names or first and maiden name of the first wife. Sorry I don't remember the source. But I bet that was limited in practice.
mary