Final answer:
In the 1500s, a Spanish governor in the New World was referred to as a corregidor, captain general, alcalde mayor, adelantado, or viceroy, depending on their jurisdiction and scope of authority.
Step-by-step explanation:
In the 1500s, a Spanish governor in the New World was referred to by several titles, depending on their specific duties and the territories they governed. The most generic term was corregidor, which designated a governor whose territory was known as a corregimiento.
In some cases, these officials might also be called captains general or alcaldes mayores. The term adelantado was used for governors of a frontier or a newly-conquered province. Furthermore, the Viceroy ruled over large areas such as New Spain, and the title Governor of the Indies was used by Columbus during his tenure.