I wonder if the “Route” column in the Irish Rail Network Statement would be a useful starting point:
This seems complete and coherent - from a quick look, every segment of the Irish Rail network would fall clearly under one and only one of these labels.
I would be more comfortable with this if I could find the same labels in use somewhere else. This is a rather technical document prepared, as far as I can see, for the theoretical possibility of another operator wanting to compete with Irish Rail. I’d prefer if there was a more public-facing source. But other uses don’t seem very systematic, e.g. the same section of line might be referred to as “DART” or “Northern Commuter” or “Dublin to Belfast” depending on the context.
(This doesn’t cover Northern Ireland obviously).