From the sleeve notes of a CD Carolan's Harp by The Harp Consort, which by coincidence I just happen to be listening to (designed to appeal to classical music lovers):-
The title planxty may perhaps have been invented by Carolan: certainly it is chiefly associated with his music. It is applied to animated pieces in jig rhythm and in a popular style....
I've heard elsewhere that when he applied the name to a piece such as "Planxty Irwin" that he was implying that Colonel John Irwin was a pretty good bloke (or maybe just paid his way for a while!)
O'Carolan is said to have been a blind Irish harpist, but I've also heard it said that he was only blind and ha'pist on Saturday nights. Irish all the time...