Abbreviate own name

Biber 0.9.4/biblatex 1.6 are now released and this should now be possible as every single name has a name hash now, in addition to the name list as a whole having a hash. See the field "hash" in section 4.2.4.1 of the biblatex 1.6 manual.

Something like this seems to work. Use the commented lines instead of those immediately below them to use a dash instead of initials.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[backend=biber,style=authoryear]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@BOOK{test1,
  AUTHOR      = {Raphael Clifford and John Doe},
  TITLE       = {Eliding My Self},
  PUBLISHER   = {Publisher},
  LOCATION    = {Elidington},
  YEAR        = {1968},
}
@BOOK{test2,
  AUTHOR      = {Brian Blinkers and Cecil Crenshaw and Raphael Clifford},
  TITLE       = {Eliding My Self Again},
  PUBLISHER   = {Publisher},
  LOCATION    = {Elidington},
  YEAR        = {1969},
}
@BOOK{test3,
  AUTHOR      = {Brian Blinkers and Raphael Clifford and Cecil Crenshaw},
  TITLE       = {Eliding My Self Once More},
  PUBLISHER   = {Publisher},
  LOCATION    = {Elidington},
  YEAR        = {1970},
}
\end{filecontents}
\addbibresource{test.bib}

\newbibmacro*{name:me}[1]{%
  \usebibmacro{name:delim}{#1}%
  \usebibmacro{name:hook}{#1}%
  \mkbibnamelast{#1}}%

\DeclareNameFormat{labelname}{%
  \iffieldequals{hash}{\mehash}%
%    {\usebibmacro{name:me}{\bibrangedash}}%
    {\usebibmacro{name:me}{#2}}%
    {\ifboolexpr{ test {\ifstrequal{#1}{Clifford}} and test {\ifstrequal{#3}{Raphael}}}
%      {\savefield{hash}{\mehash}\usebibmacro{name:me}{\bibrangedash}}%
      {\savefield{hash}{\mehash}\usebibmacro{name:me}{#2}}%
      {\ifcase\value{uniquename}%
         \usebibmacro{name:last}{#1}{#3}{#5}{#7}%
       \or
         \ifuseprefix
           {\usebibmacro{name:first-last}{#1}{#4}{#5}{#8}}
           {\usebibmacro{name:first-last}{#1}{#4}{#6}{#8}}%
       \or
         \usebibmacro{name:first-last}{#1}{#3}{#5}{#7}%
       \fi
       \usebibmacro{name:andothers}}}}%

\begin{document}
\cite{test1}\\
\cite{test2}\\
\cite{test3}
\printbibliography
\end{document}

Use the shortauthor field.

\documentclass{article}

\usepackage[style=authoryear]{biblatex}

\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@misc{C11,
  author = {Clifford, Raphael},
  shortauthor = {{---}},
  year = {2011},
  title = {How to change one's own name to a dash},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\begin{document}

Some text \autocite{C11}.

\printbibliography

\end{document}

You can define a macro for your name and place this in the bib-file. In the preamble this macro could be defined using \newcommand{\myname}{--} to add a dash instead of your name. To get a different result for the reference list you need to redefine the macro just before the list is insert, e.g. using \renewcommand{\myname}{Raphael Clifford}. However, Bib(La)TeX is then not able to parse your name into first and last name, so you won't get automatic formatting for it, but manually need to store it in the macro in the required form.