The story
From Djabugay Yirrganydji "the Yirrgay people", a derivative of Yirrgay "the Yirrgay dialect of Djabugay", itself a comitative form of a root yirrga- of unidentified meaning. Perhaps compare also Djabugay Gulunydji "the Guluy dialect of Djabugay", of identical derivation, perhaps based upon gulu "here".
Etymology from Wiktionary, CC BY-SA 4.0.