The name was Arabic but in the Moors conquering Spain there was a renaming of the people and those who lived near the Medina river were named Medina to mean the people of the city who lived near the river. This name was then brought by the conquerors of Mexico and given to the Aztecs that they had conquered. This is part of my family history. Our pronunciation is meh-de-nah other use meh-dinah.
Scripts: מדינה (Hebrew)