As of today, the Spanish census lists 3558 named Irune, as opposed to only 75 named Hirune. Hirune might seem to be the more 'correct' one for etymological reasons, but Irune is far more common even in the Basque-speaking areas. [noted -ed]
The name is actually writen 'Hirune', with an h (which in Basque, as in Spanish, has no sound). It comes from the Basque word 'hiru', that means 'three'. [noted -ed]