Was the Aztec people given their name from spanish?

Yes, the name "Aztec" was given to the people by the Spanish.

The Aztecs themselves called themselves Mexica, and their empire was known as Tenochtitlan. The name "Aztec" is derived from "Aztecá", which was a Nahuatl term used by the Spanish to refer to people from "Aztlán", a mythical homeland believed to be the origin of the Mexica.

The Spanish used the term "Aztec" because they were unfamiliar with the Mexica's own name for themselves and their empire. The term "Aztec" became more popular over time, and eventually became the dominant term used to refer to the Mexica people and their civilization.