The Aztecs called themselves Mexica. The the term Aztec was coined by an American trying to sell books in order to distinguish the older generation of Mexicans from the current one. He got the word...
To honour their gods. The aztecs thought that the sky was a sacred place so they built their temples as tall as they could in order to be able to reach the gods.
They didn't actually just become warriors, the citizens could choose if they wanted to be warriors but when there was a war going on, every citizen that was called to armas had to join the army.