Replace letter of command (control sequence)

The question is inconsistent, \expandafter\@gobble\string#1 indicates that the argument is a command sequence and the code strips the starting backslash. Then the usage cases are:

\startwiths{\plot} -> \splot
\startwithsUpper{\plot} -> \sPlot

Macro \startwithsUpper can be implemented in an expandable manner by using \@Alph instead of \uppercase for converting a simple ASCII letter to its uppercase version:

\makeatletter
\newcommand*{\startwithsUpper}[1]{%
  \csname
    s%
    \expandafter\expandafter\expandafter\FirstUpper
    \expandafter\@gobble\string#1%
  \endcsname
}
\def\FirstUpper#1{%
  \ifnum`#1>`Z % case distinction between lowercase and uppercase letter
    \@Alph{\numexpr`#1-`a+1\relax}% Convert lowercase letter
  \else
    #1% Keep uppercase letter
  \fi
}

\makeatother

% Test
\edef\x{%
  \unexpanded\expandafter\expandafter\expandafter{%
    \startwithsUpper{\plot}%
  }%
}
\makeatletter
\typeout{\string\startwithsUpper{\string\plot} -> \detokenize\expandafter{\x}}
\makeatother
\stop

Result:

\startwithsUpper{\plot} -> \sPlot

It's possible in several ways. Here's a (non expandable) one:

\documentclass{article}

\makeatletter
\newcommand{\startwithsUpper}[1]{%
  \startwithsUpper@aux#1\relax
}
\def\startwithsUpper@aux#1#2\relax{%
  \uppercase{\csname\initial@s #1}#2\endcsname
}
\def\initial@s{s}
\makeatother

\newcommand{\sPlot}{Here it is}

\begin{document}

\startwithsUpper{plot}

\end{document}

Here's an expandable one, with expl3:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewExpandableDocumentCommand{\startwithsUpper}{m}
 {
  % \use:c is essentially \csname...\endcsname
  \use:c
   {
    s % add the initial s
    \text_titlecase_first:n { #1 }
   }
 }
\ExplSyntaxOff

\newcommand{\sPlot}{Here it is}

\begin{document}

\startwithsUpper{plot}

\end{document}

The following (more complicated) version accepts either a string or a control sequence as argument.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewExpandableDocumentCommand{\startwithsUpper}{m}
 {
  \montecarlo_start_with_s_upper:n { #1 }
 }

\cs_new:Nn \montecarlo_start_with_s_upper:n
 {
  \tl_if_single:nTF { #1 }
   {
    \token_if_cs:NTF #1
     {
      \__montecarlo_start_with_s_upper:e { \cs_to_str:N #1 }
     }
     {
      \__montecarlo_start_with_s_upper:n { #1 }
     }
   }
   {
    \__montecarlo_start_with_s_upper:n { #1 }
   }
 }
\cs_new:Nn \__montecarlo_start_with_s_upper:n
 {
  \use:c
   {
    s
    \char_titlecase:N #1 
   }
 }
\cs_generate_variant:Nn \__montecarlo_start_with_s_upper:n { e }
\ExplSyntaxOff

\newcommand{\sPlot}{Here it is}

\begin{document}

X\startwithsUpper{plot}X

X\startwithsUpper{\plot}X

\end{document}

Here's a LuaLaTeX-based solution.

\documentclass{article}
\usepackage{luacode}
\begin{luacode}
function startwithsUpper ( s )
  tex.sprint ( "\\s" .. string.gsub( s , "^%l", string.upper) )
end
\end{luacode}
\newcommand\startwithsUpper[1]{\directlua{startwithsUpper(\luastring{#1})}}

\newcommand\sPlot{Hello World}  % dummy definition of "\sPlot"

\begin{document}

\startwithsUpper{plot} 

\end{document}