Traditional Naming Patterns for Both Scots & Irish People

This is the title of an article I found online at http://cotyroneireland.com/guide/NamePaterns.html.

The detail that interests me here is this:
"The only difference between the Scottish & Irish naming patterns was that when the Irish father remarries after his first wife died, the first daughter born to this new marriage was often named after the deceased wife, and included her whole name."

Having been told that the Gillespie clan considered themselves more Scotch than Irish, the relevance of this detail could be questionable. But it's still interesting to peek at the family tree and consider the two marriages of John Gillespie. The Gillespie Family Record tells us that the mother of John's children by his second marriage was Sarah Woods. Curiously we have now three pieces of documentation that record the name Jane Woods, not Sarah, as the mother of the second-marriage children. Among us cousins, we mumble "well, her name must have really been Sarah Jane Woods." Ha. We don't know what we know.

But now given this information about naming patterns, perhaps we have a clue. If Sarah Gillespie was the first-born daughter of the second marriage (we don't know for sure, perhaps she was the only surviving daughter from that marriage), then MAYBE she was named for the first wife who died (presumably died - I really have to watch my assumptions lately). Unparenthetically speaking, maybe the first wife was named Sarah?

And maybe half the answers to all my questions pertaining to the details of family history (and life?) comes in a simple reply: tradition.