It’s just tradition at this point but did have at least some significance in the past, particularly in the media who would refer to aircraft involved in newsworthy events by their individual names.
Aer Lingus does still follow the tradition of naming their perceived flagship Patrick/Pádraig from the first Lockheed Constellation to the first 720, 747 and its eventual replacement A330 in the 90s and again the latest A330 replacement.
Like with any airline, the so called flagship is more of an internal label stemming from the heritage and history of the airline rather than something passengers should take note of.