AUCTeX is a package that includes multiple TeX and LaTeX modes, but does not define an explicit AUCTeX
mode. To invoke a mode explicitly, use M-x TeX-<TAB>
or M-x LaTeX-<TAB>
to see the possibilities.
Assuming that the package is installed correctly, these tab-completions should resolve.
Various of the modes may be started automatically upon opening files with certain extensions, perhaps like myfile.tex
or similar.