Starting with package version 5.13.0, changing the secondary color normally shouldn't be necessary because it automatically adapts to the current text color. If you still want to change it, you can use \faDuotoneSetSecondary to change the color:
\documentclass[a4paper]{scrartcl}
\usepackage{xcolor}
\usepackage[pro]{fontawesome5}%
\begin{document}
Default color: \textcolor{red}{\faIcon[duotone]{university}}
\faDuotoneSetSecondary{\color{orange}}
Orange: \textcolor{red}{\faIcon[duotone]{university}}
\end{document}

Old answer
There is currently no user-level interface for this but only a code level (expl3) interface: You have to set the \l_fontawesome_duotone_secondary_style_tl token list to the commands which should be called for the secondary layer:
\documentclass[a4paper]{scrartcl}
\usepackage{xcolor}
\usepackage[pro]{fontawesome5}
\ExplSyntaxOn
\tl_set:Nn \l_fontawesome_duotone_secondary_style_tl {
\color{.!50!white} % Of course you could also load another color here
}
\ExplSyntaxOff
\begin{document}
\color{red}\faIcon[duotone]{university}
\end{document

I plan to add a proper interface in a later version, so that you will be able to set it with \fa??? {\color{secondarycolor}} but I'm not sure yet what \fa??? should be. Candidates are e.g. \faSecondaryColor, \faSetSecondary, \faSetSecondaryColor, \faDuotoneSetSecondary etc.
If you have any suggestions feel free to comment here or send me a mail.
\faIcon[duotone][secondary-color]{name}as an optional to change a single one; but a\faSetSecondaryor\faDuotoneSetSecondaryfor the global would also be nice. Finally, one could play with the tikz features of.fgand.bgas first and second colors. – Ronny Feb 17 '20 at 21:16