The American Southwest was claimed as Spanish territory. Don Francisco Cuervo y Valdez, the territory's provisional governor, petitioned the crown for permission to establish the villa of San Francisco Xavier de Alburquerque in the area in 1706. The proposed name was in honor of the Duke who was responsible for preliminary approval of Cuervo's application. The settlement was nicknamed "The Duke's City" by the original Spanish settlers, of 18 families, in an area now known as Old Town. Later, Anglo settlers shortened the name to Albuquerque leaving out the first "r".
Albuquerque was incorporated as a town in 1885 and just six years later was recognized as a city. New Mexico was admitted to the United States in 1912, becoming the 47th state in the Union. Read more about the history
here.