How to change \tablename after \begin{document}?

Question

I am writing an article in LaTeX for a Frontiers journal with MiKTeX. Their documentclass (frontiersin.org/design/zip/Frontiers_LaTeX_Templates.zip) defines \tablename as Table. I would like to change it in a section* for supplementary tables. I've yet to find a solution on this board that works.

Here is my MWE:

\documentclass[utf8]{FrontiersinHarvard}
\def\firstAuthorLast{Dodgson}
\begin{document}
\onecolumn
\section*{Main}
'Twas brillig
\begin{table}[h!]
\caption{{packages used by FrontiersinHarvard}}
\begin{verbatim}
\usepackage{parskip}[=v1] 
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage[labelsep=quad,indention=10pt]{caption}
\usepackage[labelfont=bf,list=true]{subcaption}
\end{verbatim}
\end{table}
\section*{Supplementary Tables}
\setcounter{table}{0}
\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\tablename}{Supplementary Table}
\begin{table}[h!]
\caption{Linear Coefficients.}
\begin{verbatim}
1  3 -2
2  1  4
3  5 -1
\end{verbatim}
\end{table}
\end{document}

Here is the output:

Answer 1

The class emulates the float package and also does

\def\fnum@table{Table~\thetable}

This is later used by \caption instead of \tablename in the appropriate place. Fix it.

\documentclass[utf8]{FrontiersinHarvard}
\def\firstAuthorLast{Dodgson}
% fix \tablename
\makeatletter
\renewcommand{\fnum@table}{\tablename~\thetable}
\makeatother
\begin{document}
\onecolumn
\section*{Main}
'Twas brillig
\begin{table}[h!]
\caption{{packages used by FrontiersinHarvard}}
\begin{verbatim}
\usepackage{parskip}[=v1] 
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage[labelsep=quad,indention=10pt]{caption}
\usepackage[labelfont=bf,list=true]{subcaption}
\end{verbatim}
\end{table}
\section*{Supplementary Tables}
\setcounter{table}{0}
\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\tablename}{Supplementary Table}
\begin{table}[h!]
\caption{Linear Coefficients.}
\begin{verbatim}
1  3 -2
2  1  4
3  5 -1
\end{verbatim}
\end{table}
\end{document}