I suggest you proceed as follows:
Find the file alpha.bst in your TeX distribution. Make a copy of this file and call the copy, say, alpha-mod.bst. (Don't edit an original, unrenamed file of the TeX distribution directly.)
In the file alpha-mod.bst, find the function format.names. (In my copy of the file, this function starts on line 187.)
In this function, find the following line:
{ s nameptr "{ff~}{vv~}{ll}{, jj}" format.name$ 't :=
In this line, change the string "{ff~}{vv~}{ll}{, jj}" to "{vv~}{ll}{, jj}{, f.}".
Even if you're not familiar with BibTeX's in-fix syntax, I trust you can guess what this change does: Instead of telling BibTeX to place the first name before the other components of the author's full name, BibTeX is now instructed to place a comma and the truncated first name after all other components. (Aside: In BibTeX jargon, a "full" name may have up to four components: first or given name (or names), a von-component, the surname, and a junior-component.)
Save the file alpha-mod.bst either in the directory that contains your main tex file or in a directory that's searched by BibTeX. If you choose the latter option, be sure to update the filename database of your TeX distribution suitably.
In your main tex file, change the instruction \bibliographystyle{alpha} to \bibliographystyle{alpha-mod} and perform a full recompile cycle: LaTeX, BibTeX, and LaTeX twice more to fully propagate all changes.
Happy BibTeXing.
A full MWE (minimum working example):

\documentclass{article}
\begin{filecontents}[overwrite]{mybib.bib}
@misc{ab02, author = "Anne Author and Brenda Buthor",
title = "Thoughts", year = 3002}
@misc{abc03, author = "Anne Author and Brenda Buthor and Carla Cuthor",
title = "Further Thoughts", year = 3003}
\end{filecontents}
\bibliographystyle{alpha-mod}
\begin{document}
\cite{ab02}, \cite{abc03}
\bibliography{mybib}
\end{document}
alpha.bstfrom the CTAN (Central TeX Archive Network) at http://mirrors.ctan.org/tex-archive/biblio/bibtex/base/alpha.bst. – Mico Apr 08 '20 at 10:32