How to write a command to format different letters?

Here's a straightforward solution using expl3. If you need it to work in subgroups \MyFormatter{Supermarket and \MakeUppercase{Supermarket}} you can check this solution.

\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand \myformatter { +m } { \xmllmx_myformatter:n { #1 } }
\cs_new_protected:Npn \xmllmx_myformatter:n #1
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \tl_replace_all:Nnn \l_tmpa_tl { p } { \textbf{p} }
  \tl_replace_all:Nnn \l_tmpa_tl { k } { \textbf{k} }
  \tl_replace_all:Nnn \l_tmpa_tl { m } { \textit{m} }
  \tl_replace_all:Nnn \l_tmpa_tl { t } { \textit{t} }
  \tl_use:N \l_tmpa_tl
 }
\ExplSyntaxOff

It's easy and flexible with regular expressions:

\documentclass{article}
\usepackage{xparse,l3regex}

\ExplSyntaxOn
\NewDocumentCommand{\myformatter}{m}
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \regex_replace_all:nnN
   { ([kp]+) } { \c{textbf}\cB\{ \1 \cE\} }
   \l_tmpa_tl
  \regex_replace_all:nnN
   { ([mt]+) } { \c{textit}\cB\{ \1 \cE\} }
   \l_tmpa_tl
  \tl_use:N \l_tmpa_tl
 }
\ExplSyntaxOff

\begin{document}

\myformatter{Supermarket}

\end{document}

An approach using catcodes that works if the \MyFormatter appears in the clear and is not part of an argument. As egreg pointed out in this regard, \mbox{\MyFormatter{Supermarket}} fails.

However, I jokingly retort in my comment that the way to get around the fail-case is to put the \mbox inside the MyFormatter, not the other way around. Of course, the new drawback with this "fix" is that the "m" of \mbox is now active, and so an additional \let is required: \let\MBOX\mbox\MyFormatter{\MBOX{Supermarket}}.

Finally, wipet comments that one could argue that the problem lies in the definition of \mbox, in that \hbox{\MyFormatter{Supermarket}} does not suffer the same problem.

\documentclass{article}
\let\BB\textbf
\let\II\textit
\let\CC\catcode
\let\AC\active
\let\SVP p \let\SVK k \let\SVM m \let\SVT t
\def\CODESON{\CC`p=\AC  \CC`k=\AC  \CC`m=\AC  \CC`t=\AC }
\def\CODESOFF{\CC`p=11 \CC`k=11 \CC`m=11 \CC`t=11 }
\CODESON
\def p{\BB{\SVP}}
\def k{\BB{\SVK}}
\def m{\II{\SVM}}
\def t{\II{\SVT}}
\CODESOFF
\newcommand\MF[1]{#1\CODESOFF}
\newcommand\MyFormatter{\CODESON\MF}
\begin{document}
Supermarket \MyFormatter{Supermarket} Supermarket

\mbox{\MyFormatter{Supermarket}} fails, but

\let\MBOX\mbox\MyFormatter{\MBOX{Supermarket}} works
\end{document}