Small capitals can be applied selectively using \ifcurrentname. The example below applies \textsc only to the last names of the fields labelname, author (or editor, in the absence of author). The results are demonstrated with verbose-trad1, but the solution should work for most styles.
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{csquotes}
\usepackage[american]{babel}
\usepackage[style=verbose-trad1]{biblatex}
\renewcommand*{\mkbibnamelast}[1]{%
\ifmknamesc{\textsc{#1}}{#1}}
\renewcommand*{\mkbibnameprefix}[1]{%
\ifboolexpr{ test {\ifmknamesc} and test {\ifuseprefix} }
{\textsc{#1}}
{#1}}
\def\ifmknamesc{%
\ifboolexpr{ test {\ifcurrentname{labelname}}
or test {\ifcurrentname{author}}
or ( test {\ifnameundef{author}} and test {\ifcurrentname{editor}} ) }}
\addbibresource{biblatex-examples.bib}
\begin{document}
\null\vfill\noindent
\citeauthor{aristotle:poetics,gaonkar}.
Filler text \autocites[10--15]{aristotle:poetics}{aristotle:rhetoric,companion,cicero}.
Filler text \autocites[11]{companion}[10--15]{aristotle:poetics}{aristotle:rhetoric,gaonkar,vangennep}.
\printbibliography
\end{document}

Note that applying the format to labelname makes \citeauthor set in small capitals. To avoid this under styles with citation tracking enabled, \ifmknamesc can be refined:
\def\ifmknamesc{%
\ifboolexpr{ ( test {\ifbibliography} or test {\ifbool{citetracker}} )
and ( test {\ifcurrentname{labelname}}
or test {\ifcurrentname{author}}
or ( test {\ifnameundef{author}}
and test {\ifcurrentname{editor}} ) ) }}
Under styles without tracking, \citeauthor can be modified directly:
\DeclareCiteCommand{\citeauthor}
{\boolfalse{citetracker}%
\boolfalse{pagetracker}%
\usebibmacro{prenote}}
{\ifciteindex
{\indexnames{labelname}}
{}%
\let\ifmknamesc=\ifbibliography%
\printnames{labelname}}
{\multicitedelim}
{\usebibmacro{postnote}}
To avoid use of small capitals in citations entirely, we can use the test \ifbibliography. The following definition also limits \textsc to the first author (or editor).
\def\ifmknamesc{%
\ifboolexpr{ test {\ifnumequal{\value{listcount}}{1}}
and test {\ifbibliography}
and ( test {\ifcurrentname{author}}
or ( test {\ifnameundef{author}}
and test {\ifcurrentname{editor}} ) ) }}
One style-specific consideration is the idem abbreviation. In the example it is not set in small capitals. To change this you can redefine the cite:idem bibliography macro.
\renewbibmacro*{cite:idem}{%
\textsc{\bibstring[\mkibid]{idem\thefield{gender}}}%
\setunit{\nametitledelim}}
! Undefined control sequence. \iffirstname ->\ifboolexpr { test {\ifnumequal {\value {listcount}}{1}} and ...What am I doing wrong? I've tried it with my tex file and with the code you've posted in your answer. – Gastón Sep 29 '11 at 14:59\def\iffirstnamecause I 've made a copy/paste of your code. – Gastón Sep 29 '11 at 16:23labelnamefield, not directly fromauthororeditor. Based on your example I assumed you were using theauthoryearstyle. I'll edit the answer shortly. – Audrey Oct 22 '11 at 19:00\mkbibnamefamilynow that this is required. – jcr Apr 25 '16 at 09:34\mkbibnamefamilycan't be found in the manual (v3.4) so far ... I hope that this will be fixed in v3.5. – Stefan Pinnow Apr 26 '16 at 14:12\mkbibname‘namepart’. The command is listed just below that, but misspelled\makebibnamefamily(as of v3.4)—this error seems to have already been corrected for the next release. – jcr May 01 '16 at 19:17