According to MUCH debate on another thread, it is,in fact, just "Carolan" without the "O'" if it's just the surname you use.So one refers to either ;
    A piece by Turlough O'Carolan
                or
A Carolan piece.

No,I don't get it either,but apparently some learned men who use the pen,so to speak,have deliberated,discussed,and decided thus.