The pattern varies slightly in different parts of the country.I am talking about the 19th. and early 20th. centuries.
With my mother's and my wife's families, both in Co. Cork, the first boy was named after the paternal grandfather, while the first girl was named after the paternal grandmother.The second boy was named after the maternal grandfather while the second girl was named after the maternal grandmother.
However, other places would name the first girl after the maternal grandmother, while naming the second girl after the paternal grandmother.
The third boy would be normally named after his father while the third girl would be named after her mother.
The later children would probably be named after their uncles and aunts.