Chances are Our Lady spoke to St. Juan Diego in his native tongue, Nahuatl, a language in the Aztec family. Some believe she called herself Coatlaxpeuh, which roughly translates to "who crushes the serpent".
Where did Guadalupe come from?
In Extremadura, Spain is a monastery that holds a statue of the Blessed Virgin, one of the Black Madonnas of Europe, known as Our Lady of Guadalupe. This shrine was known, and since Guadalupe sounds similar to Coatlaxpeuh, it makes sense that when San Juan Diego told them her name, they would go with Guadalupe. Puerto Rico comes to mind as an example of the Spanish altering indigenous words. The Taino people called the island Boriken, for various reasons it morphed into Borinquen. Another example is the central Puerto Rican town of Orocovis, which derives it's name from the Taino chief Orocobix.
Another name used for this apparition of Our Lady is Our Lady of Tepeyac, for it was on Tepeyac hill that she spoke to St. Juan Diego.
Santa Maria, Domina Nostra Guadalupensis, ora pro nobis paccatoribus