I believe I have found the parents of doña Isabel Álvarez Corona, the wife of conquistador don Martín Monje, giving us the origin of the above compound surnames:

1. According to his testamento, dated 16 Jun 1590, Juan Fernández Nieto was the son of conquistador Alonso Martín and doña Beatriz Álvarez, and he was married to doña Catalina de León. He mentions Martín Monje, who he identifies as his “cuñado,” so we know that Catalina de León was the daughter of don Martín Monje and doña Isabel Álvarez Corona. He names as their children Juan Fernández Corona (20), doña Catalina Corona (18), doña Beatriz Nieto (16), Martín Monje (14), and Hernán González Corona (13).
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSDL-69JN-G?cat=198356

2. Pedro de Trejo was married to doña Isabel de León, daughter of don Martín Monje and doña Isabel Álvarez Corona. On 22 May 1568, he was tried by the Holy Inquisition for “proposiciones hereticas.” Three of the witnesses presented against him were his cuñados, doña Catalina de León (age 24 and widow of miner Cristóbal de Girón), Martín Monje (19) and doña Antonia de León (14). Another witness was the above-mention Juan Fernández Nieto, who is identified as the cousin of the previous three witnesses, and nephew of doña Isabel Álvarez Corona. The obvious connection would be between her and his mother, Beatriz Álvarez, since they have the same surname (if this is so, then he and his wife, doña Catalina de León, were 1st-cousins).
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSD2-CQVJ-F?cat=31792

3. In 1554, Juan Infante accused Juan Fernández Corona and Garci Álvarez Corona of building a house and corral on his land, and he brought suit against them. At first glance, I thought that this Juan Fernández Corona was the son of Juan Fernández Nieto and doña Catalina de León, and Garci Álvarez was his cousin, the son of Martín Monje and doña Leónor de la Torre, but this would not be possible, since this lawsuit transpired between the years 1554 and 1565, before those two were born. Upon reading the document, I discovered that these two men were brothers, and were the sons of Hernán González Corona, vecinos de Guayangarao. As the two brothers were contemporaries of doña Isabel Álvarez Corona (and her supposed sister, Beatriz Álvarez), and seeing how doña Isabel had grandsons named “Garci Álvarez Corona,” “Juan Fernández Corona” and “Hernán González Corona,” I can’t help but think they are her brothers, and therefore, she is the daughter of Hernán González Corona.
https://www.familysearch.org/ark:/61903/3:1:3Q9M-CSD2-7X9C?cat=623294

4. Found at PARES/AGIS, and dated 8 Mar 1536: “Hernán González Corona and Catalina González, su mujer, con Alonso, García, Juanico, Beatriz, Leonor, Mayor e Isabel, sus hijos, vecinos de Guadalcanal, a Nueva España.”

This is undoubtedly the same Garci Álvarez Corona and Juan Fernández Corona, sons of Hernán González Corona, mentioned in the above lawsuit. While I can’t say with complete certainty that the cited daughters Beatriz and Isabel are Beatriz Álvarez and Isabel Álvarez Corona, I think it’s highly likely, given that the names of these three men appear among the descendants of both of these women. Hopefully, some day, we can find the documentation to confirm these relationships.
http://pares.mcu.es/ParesBusquedas20/catalogo/description/6049580

Saludos,
Manny Díez Hermosillo