The "Aztecs" as we call them did not refer to themselves by that name. They knew themselves as the Mexica (like mesheeca). The Mexica were but one of many Nahuatl speaking peoples living in central Mexico during the 16th century. Because of this, the "Aztecs" were mainly distinguished from all the other Nahuatl speaking peoples by their political structure, their "empire," as it were. There are still many ethnic Nahua, some who speak Nahuatl, and some who do not, living in central Mexico. There's no way to know really which of these people are descended from the Mexica, though all Nahua people are more or less modern bearers of the "Aztec" cultural/linguistic heritage.

This is somewhat tangental to your main question, but there are still in fact quite a few Mixtecs-about 500,000-800,000 I think total in Mexico(mostly in their historical homeland of Oaxaca but also in Mexico City and other regions) and a large population in New York City and southern California. The difference is more that the Mixtecs are less well-known in the US outside of those regions where they have a large diaspora like southern California. I'm also a bit put off by the "descended from Mayans" locution, since modern Mayan communities who speak Mayan languages are quite as Mayan as modern Englishmen are English or modern Scotsmen Scots.