Detect empty or null output from xstring's StrBetween

\middleinitial is not expandable, and therefore you cannot properly test whether there is a middle initial in \name or not. You'll have to store the output (the middle initial) first using the optional argument at the end of \StrBetween{<str>}{<from>}{<to>}[<macro>] and then you can check for an empty argument:

\documentclass{article}

\usepackage{xstring}

\newcommand{\name}{John Doe}

\makeatletter
\newcommand{\middleinitial}{%
  \StrBetween{\name}{ }{.}[\@middleinitial]%
}

\newcommand{\test}{%
  \middleinitial% Find middle initial
  % https://tex.stackexchange.com/q/53068/5764
  \if\relax\detokenize\expandafter{\@middleinitial}\relax
    Whoo hoo!% No middle initial
  \else
    Not whoo hoo.% A middle initial
  \fi
}
\makeatother

\begin{document}

\test % Whoo hoo.

\renewcommand{\name}{John F. Doe}%
\test % Not whoo hoo!

\end{document}

Werner already explained, why \middleinitial isn't expandable due to the usage of xstring macros.

I present a shorter way in order to test for the emptiness of \middleinitial by using \ifblank from etoolbox package. There are still two \expandafter statements required, but not a bunch of 5 of them. In addition, I find etoolbox much more convenient than ifthen or xifthen.

\expandafter\ifblank\expandafter{\middleinitial}{true branch}{false branch} is necessary, because \ifblank does not expand its first argument, i.e. without \expandafter the macro 'sees' \middleinitial, but not what the content which is stored in that macro. It must be expanded first before \ifblank performs the test.

The \expandafter primitive looks ahead of \ifblank, i.e. it ignores \ifblank first and detects the { of the first argument. Unfortunately, this is not what is desired (and not expandable anyway), so we must jump over { again, i.e.

\expandafter\ifblank\expandafter{\middleinitial}{...}{...}

will allow TeX/LaTeX to 'jump' over \ifblank to the second \expandafter, that jumps over { to \middleinitial and expands that sequence -- after this is done, TeX continues with \ifblank{expanded version of \middleinitial}{...}{...} and performs the test finally.

\documentclass{article}

\usepackage{xstring}
\usepackage{etoolbox}

\newcommand{\name}{John C.  Doe}

\newcommand{\othername}{John Doe}


\newcommand{\testinitial}[3]{%
  \begingroup
  \StrBetween{#1}{ }{.}[\middleinitial]%
  \expandafter\ifblank\expandafter{\middleinitial}{#2}{#3}%
  \endgroup
}


\begin{document}



\testinitial{\name}{Whoo hoo!}{Not whoo hoo.}

\testinitial{\othername}{Whoo hoo!}{Not whoo hoo.}

\end{document}