This is explained rather well in the document TameTheBeast. The solution is to write Theo as
{\relax Th}eo
in the bibliography file. This way {\relax Th} is treated as a single special character by the bibtex processor and in particular it is not shortened to just T when creating the abbreviation. A "special character" is any group {\...} at the top level within in an entry with first character a backslash \. The main use of this is for accented characters.

\documentclass{article}
\begin{filecontents}{\jobname.bib}
@Article{myart,
author = {Lastname, {\relax Th}eo and Surname, Sam},
title = {Title},
journal = {J. Jour.},
year = 1983,
volume = 27,
number = 2,
pages = {31--38}
}
\end{filecontents}
\begin{document}
\cite{myart}
\bibliographystyle{abbrv}
\bibliography{\jobname}
\end{document}
{\relax Th}eoin thebibfile. – Andrew Swann Feb 13 '15 at 12:01