They called themselves Mexica (pronounced [meˈʃikaʔ]). The Republic of Mexico and its capital, Mexico City, derive their names from the word Mexica. The capital of the Aztec empire was Tenochtitlan, built on a raised island in Lake Texcoco.Modern Mexico City is built on the ruins of Tenochtitlan. The Spanish colonisation of the Americas reached the mainland during the reign of Huey Tlatoani Moctezuma II (Montezuma II).hey called themselves Mexica (pronounced [meˈʃikaʔ]). The Republic of Mexico and its capital, Mexico City, derive their names from the word Mexica. The capital of the Aztec empire was Tenochtitlan, built on a raised island in Lake Texcoco.