We can modify the labelalpha-template to do this
\DeclareLabelalphaTemplate{
\labelelement{
\field[final]{shorthand}
\field{label}
\field[names=1]{labelname}
}
\labelelement{
\field[strwidth=2,strside=right]{year}
}
}
Where the important change is in the fifth line: we only print one labelname (the first), but that to its full length.
If you want to get rid of the plus indicating "et al" you need to use
\renewcommand*{\labelalphaothers}{}
Alternatively, your modification could look like this
\DeclareLabelalphaTemplate{
\labelelement{
\field[final]{shorthand}
\field{label}
\field{labelname}
}
\labelelement{
\field[strwidth=2,strside=right]{year}
}
}
With maxalphanames=1 explicitly set as an option.
MWE
\documentclass{article}
\usepackage[
style = alphabetic,
maxalphanames=1,
backend = biber,
]{biblatex}
\addbibresource{biblatex-examples.bib}
\DeclareLabelalphaTemplate{
\labelelement{
\field[final]{shorthand}
\field{label}
\field{labelname}
}
\labelelement{
\field[strwidth=2,strside=right]{year}
}
}
\renewcommand*{\labelalphaothers}{}
\begin{document}
This is plain filler \cite{wilde} and further on \cite{cicero} and \cite{baez/article}.
\end{document}