\documentclass{article}

\usepackage[utf8]{inputenc}
\usepackage[xindy]{glossaries}

\makeglossaries

\newglossaryentry{sample}{name={sample},
 description={an example}}

\newglossaryentry{S}{name={\S},
 description={section symbol}}

\newglossaryentry{alpha}{name={\ensuremath{\alpha}},
 description={alpha}}

\newglossaryentry{beta}{name={$\beta$},text={\beta},
 description={beta}}

\begin{document}
Test: \gls{sample}, \gls{S}, $\gls{alpha}$, $\gls{beta}$.

\printglossaries

\end{document}