The following example provides \newperson{<name>} which sets the name followed by an incremented counter in the form (P<num>):

\documentclass{article}
\newcounter{person}
\newcommand{\newperson}[1]{%
\refstepcounter{person}%
#1~(P\theperson)}
\begin{document}
Today I have met David~(P1) in the parking. David was friendly.
David is the father of John~(P2). Suddenly I remember he was a friend of mine, Susan~(P3).
Today I have met \newperson{David} in the parking. David was friendly.
David is the father of \newperson{John}. Suddenly I remember he was a friend of mine, \newperson{Susan}.
\end{document}
This could be expanded to use a \label-\ref system, allowing one to reference people already named (not new), for consistency. Here is such an implementation that provides \newperson[<tag>]{<name>} which can be referred to using \refperson{<tag>}. If no <tag> is supplied, <name> is used:

\documentclass{article}
\newcounter{person}
\makeatletter
\newcommand{\newperson}[2][]{%
\refstepcounter{person}% New person added
\def\@currentlabel{#2}% Update label
\@currentlabel~(P\theperson)% Set person
% https://tex.stackexchange.com/a/53091/5764
\if\relax\detokenize{#1}\relax
\label{#2}%
\else
\label{#1}%
\fi
}
\makeatother
\newcommand{\refperson}[1]{\ref{#1}}%
\begin{document}
Today I have met Davidofilofsky~(P1) in the parking. Davidofilofsky was friendly.
Davidofilofsky is the father of John~(P2). Suddenly I remember he was a friend of mine, Susan~(P3).
Today I have met \newperson[david]{Davidofilofsky} in the parking. \refperson{david} was friendly.
\refperson{david} is the father of \newperson{John}. Suddenly I remember he was a friend of mine, \newperson{Susan}.
\end{document}