Of course, \textsc{Table} should give the desired result... but unfortunately it doesn't.
That's discernible from this warning
where the default font (CMR) seems to miss the sc shape.
You may use the times package (or fourier, palatino, bookman, ...)
\documentclass{book}
\usepackage{times} %% or use {fourier} {palatino} {bookman} ...
\renewcommand{\contentsname}{\textsc{Table} of contents}
\begin{document}
\tableofcontents\addcontentsline{toc}{chapter}{\textsc{Table} of contents}
\chapter{text}
\section{text}
text
\end{document}
to get this kind of results, which I hope, is close to what you want :

\usepackage[T1]{fontenc}enables this. Thanks. – Junyong Kim Jul 28 '20 at 09:35