O Ruairc is not the name of a clan. It is an Irish surname of Norse origin (Norse Hrothrekr) and the family name was found in early times in different parts of Ireland.
The O'Rourkes of Breifney, for example, were chiefs of the clan Ui Briuin Breifne in the present counties of Leitrim and Cavan. In the 10th and 11th centuries, three of them were kings of Connacht.
They also formed part of the Ui Maine in Co. Galway. I will send you some reference material.