Did Geronimo have a last name?

No. Geronimo was actually born under the name Goyathlay, meaning "he who yawns." Because the Spanish prayed to St. Jerome, Goyathlay became known as Geronimo (cf. the Spanish name for Jerome, Jerónimo). Seeing as Geronimo is really a nickname, it is clear that he has no last name; as such, he is just called "Geronimo."