"Then the uncle manifested that it was true that on that occasion he became well and that he had seen her in the same manner as she had appeared to his nephew, knowing through her that she had sent him to Mexico to see the bishop. Also, the Lady told him that when he would go to see the bishop, to reveal to him what he had seen and to explain the miraculous manner in which she had cured him, and that she would properly be named, and known as the blessed Image, the ever-virgin Holy Mary of Guadalupe."(Nican Mopohua)

Why would the Blessed Virgin Mary appearing to a Native American of the recently conquered Aztec empire, and speaking to him in the native Nahuatl language, call herself “of Guadalupe”, a Spanish name?
Did she want to be called "de Guadalupe" because of the statue of Our Lady of Guadalupe in Estremadura, Spain?
In all apparitions of the Blessed Virgin Mary she identified herself as the Virgin Mary and phrases like Mother of God or another of Her Titles, and was later usually known by the name of the place or region where she appeared (Lourdes, Fatima).
So why should Mary, when appearing to a Native American in recently invaded Mesoamerica and speaking in the local language, want to be named with the Spanish name of Guadalupe?
Was she referring to the miraculous statue of Our Lady of Guadalupe, that was given by Pope Gregory the Great to the Bishop of Seville, Spain, was lost for 600 years and was found in 1326 by a cowherd named Gil Cordero guided by an apparition of Our Lady? This statue was named Guadalupe for the village located near the place of discovery.
The origin of the name Guadalupe has always been a matter of controversy. It is nevertheless believed that the name came about because of the translation from Nahuatl to Spanish of the words used by the Virgin during the apparition to Juan Bernardino, the ailing uncle of Juan Diego.
Some believe that Our Lady used the Aztec Nahuatl word of coatlaxopeuh which is pronounced "quatlasupe" and sounds remarkably like the Spanish word Guadalupe. Coa meaning serpent, tla being the noun ending which can be interpreted as "the", while xopeuh means to crush or stamp out. So Our Lady must have called herself the one "who crushes the serpent."

Aztec illustration. Human sacrifice to a blood thirsty god.

We must sadly remember that the Aztec priest class executed annually at least 50,000 inhabitans of the land, men, women and children, in human sacrifices to their gods. In 1487, just in a single 4 days long ceremony for the dedication of a new temple in Tenochtitlan, some 80,000 captives were killed in human sacrifice. The same practices, which in most cases included the cannibalism of the victims limbs, were common also in earlier Mesoamerican cultures, with widespread Olmec, Toltec and Maya human sacrificing rituals.

Serpent-god decorating Mesoamerican temple.

An almost universal symbol of that religion was the serpent. The temples were richly decorated with snakes. Human sacrifices were heralded by the prolonged beating of huge drums made of the skins of huge snakes, which could be heard two miles away. Nowhere else in human history had Satan, the ancient serpent, so formalized his worship with so many of his own actual symbols.
Certainly, in this case She crushed the serpent, and few years later millions of the natives converted to Christianity.