Changing the date

Question

        \documentclass[a4paper,10pt,demo    ]{article} %
    \usepackage{pifont} %bouni
    %-----accent
    \usepackage[latin1]{inputenc} %écrire directement les accents et il peut poser des problème
    \usepackage[T1]{fontenc}
      %-----
    \usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue]{hyperref}
     \usepackage{graphicx}                    % Enable pdflatex
      \usepackage{wrapfig}
      \usepackage{amsmath,amsfonts,amsthm}     % Math packages
      %%%%%%%%%%%%% dimension ancien des marges %%%%%%%%%%%%%%%%%%%%
      \usepackage{geometry}
      \geometry{left=2cm,right=2cm,top=1.5cm,bottom=1.5cm}
      %%%%%%%%%%%%% style des sections %%%%%%%%%%%%%%%%%%%%
     \frenchspacing              % Better looking spacings after periods
      \usepackage{sectsty}
      \sectionfont{%                        % Change font of \section 
         command
    \usefont{OT1}{phv}{b}{n}%       % bch-b-n: CharterBT-Bold font
     \sectionrule{0pt}{0pt}{-5pt}{1pt}}
     %%%%%%%%%%%%%%%% Macros %%%%%%%%%%%%%%%%%%%%
      \newcommand{\sepspace}{\vspace*{1em}}     % Vertical space macro
      \newcommand{\MyName}[1]{ % Name
        \Huge \usefont{OT1}{phv}{b}{n} \hfill #1
        \par \normalsize \normalfont}
      \newcommand{\MySlogan}[1]{ % Slogan}{optional)
    \large \usefont{OT1}{phv}{m}{n}\hfill \textit{#1}
    \par \normalsize \normalfont}
      %%% ------------------------------------------------------------
      \pagestyle{empty}           % No pagenumbers/headers/footers
     %%%%%%%%%%%%%%%%%%%%% Begin Document %%%%%%%%%%%%%%%%%%%%%%%%%
     \begin{document}
     %%%%%%%%%%%%%%%%%% Photo et title %%%%%%%%%%%%%%%%%%%%%%%%%
    %---------------------------
   %---------------------------
   \MyName{Name Name}
    \MySlogan{Curriculum Vitae \\ \null\hfill  (\today)}
    %\MySlogan{Curriculum Vitae (October 2016)}
    %---------------------------
    \sepspace  % Si on ajoute encore \sepspace on aura plus d'espace
    $$$$
     %%%%%%%%%%%%%% Personal details%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \section*{Informations personelles}

    \end{document}

I want to add ''th'' in the date as follows

Answer 1

The culprit is here

1. to find the right layout for your wished date (month day-with-ord, year) and
2. to change the distance between number and ord.

To test this two points please see the following MWE:

\documentclass{article}

\usepackage[en-GB,en-CA,en-US]{datetime2}

%\usepackage{etoolbox}
%\patchcmd{\DTMenglishordinal}% <cmd>
%  {#1 \DTMenglishfmtordsuffix}% <search>
%  {#1\,\DTMenglishfmtordsuffix}% <replace>
%  {}{}% <success><failure>


\begin{document}

british: 
\DTMsetstyle{en-GB}\today.
\DTMlangsetup[en-GB]{ord=raise} % ,monthyearsep={,\space},abbr
\DTMsetstyle{en-GB}\emph{\today} \today

canadian:
\DTMlangsetup[en-CA]{ord=raise} % ,monthyearsep={,\space},abbr  ,ordsep={\,}
\DTMsetstyle{en-CA}\emph{\today} \today

american:
\DTMlangsetup[en-US]{ord=raise} % ,monthyearsep={,\space},abbr
\DTMsetstyle{en-US}\emph{\today} \today

\end{document}

Its result shows you that you can choose the canadian or american variant to get your wished date layout. Because you used italic font in your document I showed in the MWE above italic and normal text for the date.

You can see that in this variant the distance between number and ord is a little bit greater than in your result, but if you want more distance, please uncomment the lines

%\usepackage{etoolbox}
%\patchcmd{\DTMenglishordinal}% <cmd>
%  {#1 \DTMenglishfmtordsuffix}% <search>
%  {#1\,\DTMenglishfmtordsuffix}% <replace>
%  {}{}% <success><failure>

in the MWE above to activate an patch. This patch adds an smal skip \, after the number (represented with #1 in the code. Now you get the result:

Okay, now we can include the found code (I choosed american variant) into your code:

\documentclass[%
  a4paper,
  10pt,
  demo
]{article}

\usepackage[en-US]{datetime2} % <=======================================
\DTMlangsetup[en-US]{ord=raise}

\usepackage{etoolbox} % <===============================================
\patchcmd{\DTMenglishordinal}% <cmd> <==================================
  {#1 \DTMenglishfmtordsuffix}% <search>
  {#1\,\DTMenglishfmtordsuffix}% <replace>
  {}{}% <success><failure>

\usepackage{pifont} %bouni

\usepackage[latin1]{inputenc} %écrire directement les accents et il peut poser des problème
\usepackage[T1]{fontenc}

\usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue]{hyperref}
\usepackage{graphicx}                    % Enable pdflatex
\usepackage{wrapfig}
\usepackage{amsmath,amsfonts,amsthm}     % Math packages

\usepackage{geometry}
\geometry{left=2cm,right=2cm,top=1.5cm,bottom=1.5cm}

\frenchspacing              % Better looking spacings after periods
\usepackage{sectsty}
\sectionfont{%                        % Change font of \section 
  command % <=================================================== ???????
  \usefont{OT1}{phv}{b}{n}%       % bch-b-n: CharterBT-Bold font
  \sectionrule{0pt}{0pt}{-5pt}{1pt}}

\newcommand{\sepspace}{\vspace*{1em}}     % Vertical space macro
\newcommand{\MyName}[1]{ % Name
        \Huge \usefont{OT1}{phv}{b}{n} \hfill #1
        \par \normalsize \normalfont}
\newcommand{\MySlogan}[1]{ % Slogan}{optional)
    \large \usefont{OT1}{phv}{m}{n}\hfill \textit{#1}
    \par \normalsize \normalfont}

\pagestyle{empty}           % No pagenumbers/headers/footers


\begin{document}

\MyName{Name Name}
\MySlogan{Curriculum Vitae \\ \null\hfill  (\DTMsetstyle{en-US}\today)} % <=======================

\sepspace  % Si on ajoute encore \sepspace on aura plus d'espace

\section*{Informations personelles}

\end{document}

with the result:

The red underlined "command" commes from the line I marked in the code with <====== ?????. Is that what you want? If not delete the line with command in the code.

Answer 2

Using datetime package, (see datetime.sty pdf, on p:8):

     \documentclass[a4paper,10pt,demo    ]{article} %
      \usepackage{datetime}
      \newdateformat{dashdate}{%
\twodigit{\THEDAY}-\twodigit{\THEMONTH}-\THEYEAR}
\newdateformat{usvardate}{%
\monthname[\THEMONTH] \ordinal{DAY}, \THEYEAR}

    \usepackage{pifont} %bouni
    %-----accent
    \usepackage[latin1]{inputenc} %écrire directement les accents et il peut poser des problème
    \usepackage[T1]{fontenc}
      %-----
    \usepackage[colorlinks=true,linkcolor=blue,urlcolor=blue]{hyperref}
     \usepackage{graphicx}                    % Enable pdflatex
      \usepackage{wrapfig}
      \usepackage{amsmath,amsfonts,amsthm}     % Math packages
      %%%%%%%%%%%%% dimension ancien des marges %%%%%%%%%%%%%%%%%%%%
      \usepackage{geometry}
      \geometry{left=2cm,right=2cm,top=1.5cm,bottom=1.5cm}
      %%%%%%%%%%%%% style des sections %%%%%%%%%%%%%%%%%%%%
     \frenchspacing              % Better looking spacings after periods
      \usepackage{sectsty}
      \sectionfont{%                        % Change font of \section 
         command
    \usefont{OT1}{phv}{b}{n}%       % bch-b-n: CharterBT-Bold font
     \sectionrule{0pt}{0pt}{-5pt}{1pt}}
     %%%%%%%%%%%%%%%% Macros %%%%%%%%%%%%%%%%%%%%
      \newcommand{\sepspace}{\vspace*{1em}}     % Vertical space macro
      \newcommand{\MyName}[1]{ % Name
        \Huge \usefont{OT1}{phv}{b}{n} \hfill #1
        \par \normalsize \normalfont}
      \newcommand{\MySlogan}[1]{ % Slogan}{optional)
    \large \usefont{OT1}{phv}{m}{n}\hfill \textit{#1}
    \par \normalsize \normalfont}
      %%% ------------------------------------------------------------
      \pagestyle{empty}           % No pagenumbers/headers/footers
     %%%%%%%%%%%%%%%%%%%%% Begin Document %%%%%%%%%%%%%%%%%%%%%%%%%
     \begin{document}
     %%%%%%%%%%%%%%%%%% Photo et title %%%%%%%%%%%%%%%%%%%%%%%%%
    %---------------------------
   %---------------------------
   \MyName{Name Name}
    \MySlogan{Curriculum Vitae \\ \null\hfill  (\usvardate\today)}
    %\MySlogan{Curriculum Vitae (October 2016)}
    %---------------------------
    \sepspace  % Si on ajoute encore \sepspace on aura plus d'espace
    $$$$
     %%%%%%%%%%%%%% Personal details%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \section*{Informations personelles}

    \end{document}

  [1]: 

Answer 3

The following uses a datetime2 approach to set the ordinal date, similar to what is proposed in ferahfeza's answer. Additionally, a minor adjustment in the placement of the ordinal is introduced:

\documentclass{article}

\usepackage[T1]{fontenc}

\usepackage{fmtcount}
\usepackage[calc,english]{datetime2}
\DTMnewdatestyle{usvardate}{%
  \renewcommand{\DTMdisplaydate}[4]{%
    \DTMmonthname{##2} \ordinalnum{##3}, \number##1 }%
  \renewcommand{\DTMDisplaydate}{\DTMdisplaydate}%
}

\makeatletter
\AtBeginDocument{
  \renewcommand{\fmtord}[1]{\,\fc@textsuperscript{#1}}% Add \, before ordinal number
}
\makeatother

\newcommand{\MyName}[1]{ % Name
  \Huge \usefont{OT1}{phv}{b}{n} \hfill #1
  \par \normalsize \normalfont}
\newcommand{\MySlogan}[1]{ % Slogan}{optional)
  \large \usefont{OT1}{phv}{m}{n}\hfill \textit{#1}
  \par \normalsize \normalfont}

\begin{document}

\MyName{Name Name}
\MySlogan{Curriculum Vitae \\ \null\hfill  (\DTMsetdatestyle{usvardate}\today)}

\end{document}