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author      = {{Marcus Tullius Cicero}},
sortname    = {Cicero, Marcus Tullius},
shortauthor = {Cicero},% für 'Cicero' statt 'Marcus Tullius Cicero' in Zitaten

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{filecontents}

\begin{filecontents*}{ancientroman.dbx}
\DeclareDatamodelConstant[type=list]{nameparts}{prefix,family,suffix,given,praenomen,nomen,cognomen}% the last three are for ancient Roman names
\end{filecontents*}

\begin{filecontents*}{\jobname.bib}
@book{bellgall,
  author      = {praenomen=Marcus, nomen=Tullius, cognomen=Cicero, sortnamekeyscheme=ancientroman},
  title       = {Commentarii de Bello Gallico},
  shortttitle = {De Bello Gallico},
  date        = {1983},
}
@book{natdeo,
  author       = {praenomen=Marcus, nomen=Tullius, cognomen=Cicero, sortnamekeyscheme=ancientroman},
  title        = {De natura deorum. {\"U}ber das Wesen der G{\"o}tter},
  date         = 1995,
  editor       = {Blank-Sangmeister, Ursula},
  translator   = {Blank-Sangmeister, Ursula},
  afterword    = {Thraede, Klaus},
  language     = {langlatin and langgerman},
  publisher    = {Reclam},
  location     = {Stuttgart},
}
\end{filecontents*}

\usepackage[style=authoryear-icomp,datamodel=ancientroman]{biblatex}

\addbibresource{biblatex-examples.bib}
\addbibresource{\jobname.bib}

% sort 'Marcus Tullius Cicero' under 'Cicero -> Tullius -> Marcus'
\DeclareSortingNamekeyScheme[ancientroman]{
  \keypart{
    \namepart{cognomen}
  }
  \keypart{
    \namepart{nomen}
  }
  \keypart{
    \namepart{praenomen}
  }
}


\DeclareNameAlias{sortname}{family-given}

% given-family gives 'Marcus Tullius Cicero' in full
\DeclareNameFormat{given-family}{%
  \ifsortnamekeyscheme{ancientroman}
    {\usebibmacro{name:ancientroman-full}
       {\namepartpraenomen}
       {\namepartnomen}
       {\namepartcognomen}}
    {\ifgiveninits
       {\usebibmacro{name:given-family}
         {\namepartfamily}
         {\namepartgiveni}
         {\namepartprefix}
         {\namepartsuffix}}
       {\usebibmacro{name:given-family}
         {\namepartfamily}
         {\namepartgiven}
         {\namepartprefix}
         {\namepartsuffix}}}%
  \usebibmacro{name:andothers}}

% family-given also gives 'Marcus Tullius Cicero' in full (no inversion here!)
\DeclareNameFormat{family-given}{%
  \ifsortnamekeyscheme{ancientroman}
    {\usebibmacro{name:ancientroman-full}
       {\namepartpraenomen}
       {\namepartnomen}
       {\namepartcognomen}}
    {\ifgiveninits
       {\usebibmacro{name:family-given}
         {\namepartfamily}
         {\namepartgiveni}
         {\namepartprefix}
         {\namepartsuffix}}
       {\usebibmacro{name:family-given}
         {\namepartfamily}
         {\namepartgiven}
         {\namepartprefix}
         {\namepartsuffix}}}%
  \usebibmacro{name:andothers}}

% labelname (used in citations) uses 'Cicero' only
\DeclareNameFormat{labelname}{%
  \ifsortnamekeyscheme{ancientroman}
    {\usebibmacro{name:ancientroman-short}
       {\namepartpraenomen}
       {\namepartnomen}
       {\namepartcognomen}}
    {\ifcase\value{uniquename}%
       \usebibmacro{name:family}
         {\namepartfamily}
         {\namepartgiven}
         {\namepartprefix}
         {\namepartsuffix}%
     \or
       \ifuseprefix
         {\usebibmacro{name:given-family}
           {\namepartfamily}
           {\namepartgiveni}
           {\namepartprefix}
           {\namepartsuffixi}}
         {\usebibmacro{name:given-family}
           {\namepartfamily}
           {\namepartgiveni}
           {\namepartprefixi}
           {\namepartsuffixi}}%
     \or
       \usebibmacro{name:given-family}
         {\namepartfamily}
         {\namepartgiven}
         {\namepartprefix}
         {\namepartsuffix}%
     \fi}
  \usebibmacro{name:andothers}}


\newbibmacro*{name:ancientroman-short}[3]{%
  \mkbibromancognomen{#3}}%

\newbibmacro*{name:ancientroman-full}[3]{%
  \usebibmacro{name:delim}{#1#2#3}%
  \usebibmacro{name:hook}{#1#2#3}%
  \ifdefvoid{#1}{}{\mkbibromanpraenomen{#1}\isdot}%
  \ifdefvoid{#2}{}{\bibnamedelimd\mkbibromannomen{#2}\isdot}%
  \ifdefvoid{#3}{}{\bibnamedelimd\mkbibromancognomen{#3}\isdot}}

\let\mkbibromancognomen\mkbibnamefamily
\let\mkbibromannomen\mkbibnamegiven
\let\mkbibromanpraenomen\mkbibnamegiven

\begin{document}
\textcite{bellgall,natdeo,sigfridsson,knuth:ct:a,coleridge,averroes/hercz}
\printbibliography
\end{document}