Alzaga is a surname of Basque origins. Notable people with the surname include:

Fernando Vérgez Alzaga (born 1945), Spanish bishop Martín de Álzaga (1755–1812), Spanish merchant and politician Martín de Álzaga (racing driver) (1901–1982), Argentine racing driver Óscar Alzaga (born 1942), Spanish politician Rodolfo de Álzaga (1930–1994), Argentine racing driver