How did the Native American get this name?

While it is not known for sure how the Native American,Goyathlay, came to be called "Geronimo" this theory is at least based on facts and believable.

Goyathlay was indeed a fearsome individual with numerous deaths that some would call murders to his 'credit.' He and his band ranged on both sides of the Rio Grande leaving many dead Americans and Mexicans behind them and some say they caused much more havoc on the Mexican side. One of his unique methods of attack was to leap out from seemingly nowhere causing great fear and confusion upon his intended victims. It was during one such surprise attack of Mexicans that an American 'Gringo' along with them heard some of the Mexicans exclaim "GERONIMO!" They were calling upon Saint 'Geronimo' [St. Jerome] for protection as he was one of the patron saints of Mexican and Spanish soldiers and they would regularly shout his name when charging into battle. (Anglos are often heard to exclaim; "OH GOD!" under similar circumstances.) That Gringo, who was ignorant of Hispanic and Roman Catholic culture, thought they were calling out the Indian's name and survived to tell 'that story' far and wide.

In those days the average Mexican probably could not read Latin but they were well aware that it was the language of  'The Church.' Every Mass and Service was held in Latin and all of their padres read from a Latin Bible, The Vulgate, that Saint Jerome ['Geronimo' to them] translated from the original Hebrew and Greek. Because of this alone, they held St. 'Geronimo' or simply 'Geronimo' in very high esteem and honored him by naming many creeks, hills, mesas and towns for him.