I'd suggest using the following redefinition of cite:full:
\renewbibmacro*{cite:full}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver
{\DeclareNameAlias{sortname}{labelname}}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
cite:full in the verbose styles normally just prints the whole bibliography entry as it would be printed in the bibliography, but before that it changes sortname to default (\DeclareNameAlias{sortname}{default}), so we get names in first-last format (as that is what default is set to ... by default).
We simply change sortname to labelname, so we get last names if possible and unambiguous names otherwise (depending on the uniqeuname option; anyway, the name format will be the same as in subsequent citations).
If you insist on last names no matter what, I'd suggest
\DeclareNameFormat{family}{%
\usebibmacro{name:family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}%
\usebibmacro{name:andothers}}
\renewbibmacro*{cite:full}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver
{\DeclareNameAlias{sortname}{family}}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
Edited for the new name format in biblatex >= 3.3, see edit history for pre-3.3 code.
MWE
\documentclass{beamer}
\usetheme{Boadilla}
\usepackage{chngcntr}
\usepackage{lmodern}
\usepackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@article{Brav2002,
author = {Alon Brav and J. B. Heaton},
title = {Competing Theories of Financial Anomalies},
journal = {Reveiw of Financial Studies},
year = {2002},
volume = {15:2},
pages = {575-606},
}
\end{filecontents*}
\usepackage[backend=bibtex,style=verbose]{biblatex}
\addbibresource{\jobname.bib}
\renewbibmacro{in:}{\hspace{-5pt}}
\AtEveryCitekey{\clearfield{pages}\clearfield{volume}}
\renewbibmacro*{cite:full}{%
\usebibmacro{cite:full:citepages}%
\printtext[bibhypertarget]{%
\usedriver
{\DeclareNameAlias{sortname}{labelname}}
{\thefield{entrytype}}}%
\usebibmacro{shorthandintro}}
\begin{document}
\begin{frame}
\frametitle{Stuff famous linguists asked}
\begin{block}{A block}
\begin{enumerate}
\item Is it part?\footcite{Brav2002}
\item More Saussure.\footcite{Brav2002}
\end{enumerate}
\end{block}
\end{frame}
\end{document}

usebibmacro{name:last}which in some way I think has been replaced withusebibmacro{name:family}still works? I think the arguments it takes must have changed, because as is, it results inIllegal parameter number in definition of \blx@defformat@d– EngBIRD Jun 24 '16 at 22:28\DeclareNameFormat{family}{% \usebibmacro{name:family} {\namepartfamily} {\namepartgiven} {\namepartprefix} {\namepartsuffix}% \usebibmacro{name:andothers}}(modulo line breaks). See above. – moewe Jun 25 '16 at 06:28cite:fullshould go in the.cbx-file properly specified withcitestyle=... Your solution is neat, but it took me many long hours to figure out how to apply it :/ – nJGL Mar 26 '19 at 17:12.cbxfiles. – moewe Mar 26 '19 at 17:28