The most famous person with this combination of names was don Fernando de Alva Cortés Ixtlilxochitl, a chronicler. He was born in Tetzcoco possibly around 1568, and died in Mexico City in 1648. He possibly lived for a time in San Juan Teotihuacan, too. He claimed to be a direct descendent of the Acolhua governing line of Tetzcoco. He may have been a castizo (three parts Spanish, one part Nahua). He learned Nahuatl at the Colegio de la Santa Cruz de Tlatelolco.
https://es.wikipedia.org/wiki/Fernando_de_Alva_Ixtlilx%C3%B3chitl
His History of the Chichimeca Nation was lost in the 1820s and rediscovered by librarian Wayne Ruwet (UCLA) in the British and Foreign Bible Society in the 1980s. It appeared in print in 2019, edited and translated by Amber Brian, Bradley Benton, Peter B. Villella, and Pablo García Loaeza, and published by the University of Oklahoma Press. These authors give the birth of don Fernando de Alva Ixtlilxochitl at 1578 and his death at about 1650.
Don Fernando de Alva Ixtlilxochitl was an older brother of Bartolomé de Alva, who entered the priesthood in Mexico City in 1625 and, in 1634, published a Nahuatl-language confessionary.
Bartolomé de Alva, A Guide to Confession Large and Small in the Mexican Language, 1634, eds. Barry D. Sell and John Frederick Schwaller, with Lu Ann Homza (Norman: University of Oklahoma Press, 1999), 13.