EDIT solution simplified and new alternative solution added, more comprehensive examples added
You can add a colour when registering the author by putting the color before the author tag:
\FXRegisterAuthor{sv}{asv}{\color{red}Me}
Here is a sample demonstrating various of the fixme formats, its list of fixmes and the index:


\documentclass[11pt]{article}
\usepackage{xcolor}
\usepackage[draft,inline,nomargin,index]{fixme}
\fxsetup{theme=color,mode=multiuser}
\FXRegisterAuthor{sv}{asv}{\color{red}Me}
\FXRegisterAuthor{aa}{aaa}{\color{green}Other}
\usepackage{makeidx}
\makeindex
\begin{document}
\svnote{This is me} and \aanote{This is other}.
Probably\sverror{A dire mistake.} a good thing. \aawarning*{Watch out!}{This
is trivial.} Oh no \aafatal{Die!}
\begin{svnote}[margin]{Explanation}
A longer note that tries to explain something or other, but I can't
remember what.
\end{svnote}
\listoffixmes
\printindex
\end{document}
For example, the inline notes are set via the \FXLayoutInLine which takes three arguments Type (error, etc.), Note and Author. The third field Author is the last argument registered under the author, and is used unchanged in the note, so its color affects the rest of the text.
Alternatively you might just like to change the colour/background of the author identifier, keeping the color themes colours for the actually note text, as follows:

\documentclass[11pt]{article}
\usepackage{xcolor}
\usepackage[draft,inline,nomargin,noindex]{fixme}
\fxsetup{theme=color,mode=multiuser}
\FXRegisterAuthor{sv}{asv}{\colorbox{red}{\color{black}Me}}
\FXRegisterAuthor{aa}{aaa}{\colorbox{green}{\color{black}Other}}
\begin{document}
\svnote{This is me} and \aanote{This is other}.
Probably\sverror{A dire mistake.} a good thing. \aawarning*{Watch out!}{This
is trivial.} Oh no \aafatal{Die!}
\begin{svnote}[margin]{Explanation}
A longer note that tries to explain something or other, but I can't
remember what.
\end{svnote}
\listoffixmes
\end{document}
Unfortunately this alternative version does not work with the index.