This gets described on page 12 of the siunitx manual:
New units are produced using the \DeclareSIUnit macro. < symbol > can
contain literal input, other units, multiple prefixes, powers and
\per, although literal text should not be intermixed with unit
macros. Units can be created with < options > from the usual list
understood by siunitx, and apply the specific unit macro only.
% arara: pdflatex
\documentclass{article}
\usepackage{siunitx}
%\sisetup{per-mode=symbol} % for the slashed version.
\DeclareSIUnit{\sample}{S}
\begin{document}
I would like to write something like \SI{1}{\giga\sample\per\second}
Problem could arise if you need to give some numbers in \si{\siemens}
\end{document}
