Second optional argument for newcommand to be the same of the first in case it is not specified

The standard \newcommand doesn't support it. The kernel provides \@dblarg:

\makeatletter
\newcommand{\mypar}{\@dblarg\@mypar}
\def\@mypar[#1]#2{#2\paren{#1}}
\makeatletter

However, you can do it more robustly and easily with xparse:

\usepackage{xparse}

\NewDocumentCommand{\mypar}{O{#2}m}{#2\paren{#1}}

Full example:

\documentclass{article}
\usepackage{xparse}

\newcommand{\paren}[1]{\left(#1\right)} %this is just an example command

\NewDocumentCommand{\mypar}{O{#2}m}{#2\paren{#1}}

\begin{document}

$\mypar{a}$

$\mypar[b]{a}$

\end{document}

Not that I endorse that definition of \paren, of course. ;-)

The latex format has a standard command for doubling an optional argument in this way (as used for \section[zz]{zz})

\documentclass{article}


\newcommand{\xmypar}[2][]{#2\left(#1\right)} %this is just an example command

\makeatletter
\newcommand\mypar{\@dblarg\xmypar}
\makeatother

\begin{document}

$\mypar{a}$

$\mypar[b]{a}$

\end{document}

You can check for an empty argument in #1 and use it to condition on displaying either #1 or #2:

\documentclass{article}

\usepackage{mleftright}

\newcommand{\paren}[1]{\mleft(#1\mright)} %this is just an example command
\newcommand{\mypar}[2][]{%
  \if\relax\detokenize{#1}\relax #2\else #1\fi\paren{#2}}

\begin{document}

$A = \mypar{a} = \mypar[a]{a} \neq \mypar[b]{a}$

\end{document}

The following definition is a little simpler, but also works:

\newcommand{\mypar}[2][\relax]{%
  \ifx\relax#1\relax #2\else #1\fi\paren{#2}}