I think the name is rare as the usual spelling is O'Hierlihy. The "O" is supposed to be from "Ua" and to mean something like, "from the family of." I vaguely recall that without the "O", means the direct family. My own connection is through Ellen or Helen Hierlihy, b. ca. 1832, d/o James William and Louisa (Urquhart) Hierlihy; who m. my great great grandfather, John Murray (b. ca. 1832, d. Tabusintac 23APR1915), s/o Hugh and Jane (Anderson) Murray. Don't know much about Ellen (or Helen) though.