How to replace characters from jobname?

Apart from expl3, you can also use StrSubstitute with the option to save the result in a macro. Note that you need to convert _ to the right catcode, for example using \string.

MWE:

\documentclass{article}
\usepackage{xstring}

\title{\textbf{\subfinal}}
\author{}
\date{}

\begin{document}
\StrSubstitute{\jobname}{-}{: }[\subsemi]
\StrSubstitute{\subsemi}{\string_}{ }[\subfinal]
\maketitle
The name of the tex file is {\tt{Chap-Name\_of\_Section.tex}}. I am running {\verb|pdflatex|} on the tex file. After using {\verb|\jobname|} I get the title.

I want to print the title as ``Chap: Name of Section''. Note that `-' sign is to be replaced by `:' followed by a single space and underscores (`\_') are to be replaced by spaces.
\end{document}

Result:

Same idea as in @jakun's answer, but implemented (without packages, also) in a way which is easier (more convenient, rather, as it takes less space) to extend to more special characters. Expandable, too.

\documentclass{article}

\long\def\DoThis #1#2\OrThat #3{\fi #1}
\makeatletter
\let\OrThat\@firstofone
\makeatother

\begingroup
  \makeatletter
  \catcode`_=12 % other
% if using Babel with a language that makes : a shorthand (French, e.g.)
% then you need  \catcode`: \active here and \DoThis{\noexpand: }
  \def\myParser#1{%
     \ifx\relax#1\DoThis{\@gobble}\fi
     \ifx -#1\DoThis{: }\fi
     \ifx _#1\DoThis{ }\fi
     \OrThat{#1}\myParser
  }%
  \xdef\parsedJobname{\expandafter\myParser\jobname\relax}
\endgroup

\title{\parsedJobname}

\begin{document}
    \maketitle
    The parsed jobname is ``\parsedJobname''.
\end{document}

If the above is file Test_Titre-Un.tex then the result is

Code for French as per code comment.

\begingroup
  \makeatletter
  \catcode`_=12 % other
  \catcode`\: \active 
  \def\myParser#1{%
     \ifx\relax#1\DoThis{\@gobble}\fi
     \ifx -#1\DoThis{\noexpand: }\fi
     \ifx _#1\DoThis{ }\fi
     \OrThat{#1}\myParser
  }%
  \xdef\parsedJobname{\expandafter\myParser\jobname\relax}
\endgroup

Produces (using babel+french):

Here is more simple, format independent, expandable solution:

\def\cnvjobname{\expandafter\cnvjobnameA\jobname\relax}
\def\cnvjobnameA#1{\ifx\relax#1\else
   \ifx-#1: \else \expandafter\ifx\string_#1 \else #1\fi\fi
   \expandafter\cnvjobnameA\fi
}

%test:
\message{... "\cnvjobname"}

\bye