As NewMexiKen notes below, “Several sources give June 16, 1829, as Geronimo’s date of birth.” In her excellent 1976 biography of Geronimo, however, Angie Debo concludes:
Geronimo was born in the early 1820’s near the upper Gila in the mountains crossed by the present state boundary [Arizona-New Mexico], probably on the Arizona side near the present Clifton. …
He was given the name Goyahkla, with the generally accepted meaning “One Who Yawns,’ why or under what circumstances is not known.
As an adult in battle he was called Geronimo by Mexican soldiers, perhaps because they could not pronounce Goyahkla, or perhaps to invoke Saint Jerome (Geronimo is Spanish for Jerome). The name was adopted for him by his own people.