Right.
The city that the Spaniards built on the ruins of Tenochtitlan was named Mexico City.
1519
The Spaniards main town in Mexico was Tenochtitlan, the capital of the Aztec Empire. The Spaniards led by Hernan Cortes conquered Tenochtitlan in 1521, leading to the fall of the Aztec Empire.
Mexico City
1520
That would be Mexico City; built by the Spaniards.
The Spanish desroted Tenochtitlan in 1535
It was razed and became the capital of the New Spain colony.
Emperor Montezuma
Their Tlaxcalan allies
It was then destroyed in 1575 by the Spaniards.
The Spanish destroyed Tenochtitlan by having a war for 3 months inside the city. The biggest thing that brought them down, however, was smallpox that the Aztecs were not immuned to.