Answer:
The new settlement was named after the Presidio San Antonio de Béjar, the Spanish military outpost that protected the missions. The presidio, located at the San Pedro Springs, was founded in 1718 and named for Viceroy Balthasar Manuel de Zúñiga y Guzmán Sotomayor y Sarmiento, second son of the Duke of Béxar (a city in Spain). Bexar is pronounced "Bear"