The Aztecs were actually called Mexica
The Mexica or Mexicas — called Aztecs in occidental historiography, although this term is not limited to the Mexica — were an indigenous people of the Valley of Mexico, known today as the rulers of the Aztec empire.
The Mexica were a Nahua people who founded their two cities Tenochtitlan and Tlatelolco on raised islets in Lake Texcoco around AD 1200. After the rise of the Aztec Triple Alliance, the Tenochca Mexica (that is, the inhabitants of Tenochtitlan), assumed a senior position over their two allied cities — Tlatelolco and Tlacopan.
The Mexica are eponymous of the placename Mexico Mēxihco, This refers to the interconnected settlements in the valley which became the site of what is now Mexico City, which held natural, geographical, and population advantages as the metropolitan center of the region of the future Mexican state. This area was expanded upon in the wake of the Spanish conquest and administered from the former Aztec capital as New Spain.