Option caption enhances the listing with a caption, whose title is also used for the entry in the list of listings:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\lstset{language = Matlab, inputpath=./Code/}
\begin{document}
\lstlistoflistings
\lstinputlisting[caption=test1.m]{test1.m}
\lstinputlisting[caption=test2.m]{test2.m}
\lstinputlisting[caption=test3.m]{test3.m}
\end{document}

The caption can be suppressed for the document by an empty mandatory argument for key caption. The optional argument in square brackets denotes the title for the entry in the list of listings:
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\lstset{language = Matlab, inputpath=./Code/}
\begin{document}
\lstlistoflistings
\lstinputlisting[caption={[test1.m]{}}]{test1.m}
\lstinputlisting[caption={[test2.m]{}}]{test2.m}
\lstinputlisting[caption={[test3.m]{}}]{test3.m}
\end{document}

matlab-prettifierpackage; see this answer. – jub0bs Aug 06 '16 at 15:13