What is the nickname of Ecuador?

Perhaps by nickname, you mean motto. In that case, the offical motto of Ecuador is "Dios, Patria, y Libertad" which translates to "God, Homeland, and Liberty". Some more informal 'mottos' heard in popular culture nowadays in Ecuador include "Ya la patria es de todos!" or "Estamos en marcha!". People sometimes also refer to Ecuador (and more specifically the capital city of Quito) as "El Mitad del Mundo" or "Center of the World" steming from its location on the equator.