Flora and Katie -- my mum's parents (in Ireland) used a family hierarchy system to name their children: first boy, grandad's father, first girl, grandad's mother; second boy and girl, named after grandad's aunt and uncle from whom he inherited the farm as they were childless and he had worked it since age 14 alongside his uncle; third boy, granny's long dead father, third girl, granny's long dead mother (she was orphaned at a young age); remaining two children (boys), brothers of grandad's as granny had lost touch with her biological relatives.
The normal custom in their neck of the woods was to use first the father's parents' names, then the mother's parents' names, and other family names from each side once there were two girls and two boys, or while waiting for two of each. They adapted the custom to their own circumstances.
Names in that particular area tended to come from a fairly small pool of names, though within that pool there were some that are unusual. So you would have Michael, James, Patrick, John, Brigid, Anne/Anna, Mary, Margaret and the like, and then names like Laserian, Moling, Anastatia and Moses.