O'Carolan....Means Grandson of Carolan...in English translation....
McCarolan would be Son of...
an "O" prefixed Irish Names are Older than "Mac" or "Mc"...as seen in The Name O'Brien...Many of whom supposedly descent from Brian Buru..and It was around his time Irish Surnames came to exist...1000 odd years ago
Many Gaelic Dropped the O as seen in names such as "Scottish Neill"...Rielly...Rourke...Sullivan...Kane....Connor....Kelly...Lunney...Lynch ...Gorman....Boyle...Laughlin....Malley...Flaherty...Flynn....Dowd....Haire.....Madden ...Donoghue....Riordan....Donovan....Moore (More)....etc etc etc