I'm trying the following:
\documentclass{article}
\newcounter{testcounter}
\def\teststring{begin}
\begin{document}
\stepcounter{testcounter}
\def\newstring{\expandafter\string\csname\teststring-middle-\thetestcounter\endcsname}
\thetestcounter
\teststring
\newstring
\end{document}
And the result is the following:
So, I don't know where the " comes from. The above example is just a demo. The concatenated string \newstring´´ will later be used inside a \label command.
Any hints are welcome!

\expandafter\string\csnameand\endcsnameand possibly use\edefinstead of\def, depending on what you want. – David Carlisle Aug 01 '16 at 11:17