What did the land conquered by Spain become known as?

The lands conquered by Spain were known as the Spanish Empire.

In 1535 the Spanish crown created the Viceroyalty of New Spain which comprised the Spanish territories in the Septentrion, the northern hemisphere. In the US it comprised California, Arizona, New Mexico, Nevada, Utah and most of Colorado and Mexico; from 1763 to 1800 it also included French Louisiana (Montana, South Dakota, Iowa, Nebraska, Kansas, Missouri, Oklahoma, Arkansas, Louisiana, part of South Dakota, Minnesota, Wisconsin and Colorado and a small slice of Texas). It also included Central America, the islands of Cuba and Santo Domingo, Venezuela and the Philippines.

The Viceroyalty of Peru, created in 1542, comprised the Spanish territories in the southern hemisphere; the colonies in South America except for Venezuela.

The Spanish colonial provinces in northern South America came under the New Kingdom of Granada, which was created in the 1538. It comprised present day Colombia and part of Venezuela and was governed by the president of the Audencia of Bogota. It was originally part of the Viceroyalty of Peru until 1717 when it became Viceroyalty of New Granada. This viceroyalty was comprised of a core area (Colombia, Panama, Ecuador, and Venezuela) and Costa Rica, Nicaragua, Guyana, south-western Suriname, parts of north-western Brazil, and northern Peru. Although Guyana was formally part of this viceroyalty, the Dutch were the first to establish colonial settlements: Essequibo (1616), Berbice (1627), and Demerara (1752). They ceded the settlements to the British in 1814 and were joined together, forming British Guyana in 1831.