Does the variable maker work only with latin letters and numbers?

Question

How can I make the variable for non-Latex user, for example, using the \newcommand{}{} with parameters? For example, I want the user change only the word in newcommand description and it will change in whole document automatically?

\newcommand{\R}{My system}
...
\section{Introduction}
Here I would like to introduce \( \R \)
...
   \begin{table}[]
       \centering
       \begin{tabular}{c|c}
           \( \R \) &  \\
                    & 
       \end{tabular}
       \caption{Caption}
       \label{tab:my_label}
   \end{table}

This doesn't work with Russian letters (\usepackage[russian,english]{babel} and \selectlanguage{russian} is added and in usage)

Ok, posting the full example where I don't get anything (blank space instead of russian word):

\documentclass{article}
%\documentclass{ICD}
\usepackage[T2A,T1]{fontenc}

\usepackage[utf8]{inputenc}
\usepackage{multicol}
%\usepackage[russian,english]{babel}
\usepackage[russian]{babel}
\usepackage{multirow}   %для таблиц со слиянием столбцов и строк
\usepackage{amsthm}
\usepackage{array}      %для таблиц с заданной шириной столбца
\usepackage{float}
\usepackage[table]{xcolor}
%\setlength{\arrayrulewidth}{1mm}
%\setlength{\tabcolsep}{18pt}
%\renewcommand{\arraystretch}{2.5}
%\newcolumntype{s}{>{\columncolor[HTML]{AAACED}} p{3cm}}
%\arrayrulecolor[HTML]{DB5800}

\ProcessOptions

\begin{document}
%\hoffset = 20pt
%\maketitle
\selectlanguage{russian}


\tableofcontents


\newcommand{\Mysyst}{ \begin{center} \selectlanguage{russian} система \end{center}}

 \section{Introduction}
    Here I would like to introduce \( \Mysyst \)
    ...
       \begin{table}[]
           \centering
           \begin{tabular}{c|c}
               \( \Mysyst \) &  \\
                        & 
           \end{tabular}
           \caption{Caption}
           \label{tab:my_label}
       \end{table}


\end{document}

Answer 1

New answer after the MWE

1. You are using \( and \) delimiter here --- they enter mathematical mode. I do not read russian, but I think that система is not a formula, isn't it? If you want to typeset it in italic or slanted) font, use \textit (or \emph, or \textsl, depending on the objective). In math mode you can have just formulas: https://www.learnlatex.org/en/lesson-10

2. I do not get what you want to obtain with the \begin{center}...\end{center} there. In the tabular, the text is already centered. And there is no sense in "centering" inside a paragraph, like you are trying to do in the first line of text.

3. \ProcessOptions is for package creators, not user, avoid it. And you have to specify where you want your floating, so I added [ht] (you should have had a warning).

Correct those and you have:

\documentclass{article}
\usepackage[T2A,T1]{fontenc}

\usepackage[utf8]{inputenc}
\usepackage{multicol}
\usepackage[russian]{babel}
\usepackage{multirow}   %для таблиц со слиянием столбцов и строк
\usepackage{amsthm}
\usepackage{array}      %для таблиц с заданной шириной столбца
\usepackage{float}
\usepackage[table]{xcolor}


\begin{document}
\selectlanguage{russian}


\tableofcontents

% Additional braces to confine the effect of selectlanguage
\newcommand{\Mysyst}{{\selectlanguage{russian} система}}

 \section{Introduction}
    Here I would like to introduce \emph{\Mysyst}
    ...
       \begin{table}[ht]
           \centering
           \begin{tabular}{c|c}
               \Mysyst &  \\
                        & 
           \end{tabular}
           \caption{Caption}
           \label{tab:my_label}
       \end{table}

\end{document}

Original answer

Just to show you why an MWE is really necessary in LaTeX to understand the problem: this snippet:

\documentclass[a4paper,11pt]{article}
\usepackage[spanish, english]{babel}
\newcommand{\R}{The letter ``ñ''} 
\begin{document}
\section{Introduction}
Here I would like to introduce \emph{\R}

   \begin{table}
       \centering
       \begin{tabular}{c|c}
           \emph{\R} &  \\
                    & 
       \end{tabular}
       \caption{Caption}
       \label{tab:my_label}
   \end{table}

\end{document}

works perfectly, giving

...so we are at a loss to say where your problem really is.