If the number of the chapter should not be displayed in the headings use
\renewcommand*{\chapterformat}{}
But if you want a prefix line for the chapter headings use class option chapterprefix and
\renewcommand*{\chapterformat}{%
\mbox{\chapappifchapterprefix{\nobreakspace}\thechapter\autodot:
\IfUsePrefixLine{}{\enskip}}%
}
to add the colon after the number.
To change the format of the entry in the page header use
\renewcommand*{\chaptermarkformat}{\chapapp\ \thechapter\autodot:\enskip}
and for the TOC entry
\let\originaladdchaptertocentry\addchaptertocentry
\renewcommand*{\addchaptertocentry}[2]{%
\IfArgIsEmpty{#1}
{\originaladdchaptertocentry{#1}{#2}}
{\originaladdchaptertocentry{\chapappifchapterprefix{\nobreakspace}#1\autodot}{#2}}%
}
\RedeclareSectionCommand[
tocentrynumberformat={\def\autodot{:}},
tocdynnumwidth
]{chapter}
Example:
\documentclass[
12pt,
chapterprefix,% use a prefix line for chapters
numbers=noenddot% no dot at the end of numbers
]{scrreprt}
\usepackage{lipsum}% only for dummy text
\pagestyle{headings}
\renewcommand*{\chapterformat}{%
\mbox{\chapappifchapterprefix{\nobreakspace}\thechapter\autodot:
\IfUsePrefixLine{}{\enskip}}%
}
\renewcommand*{\raggedchapter}{\centering}
\renewcommand*{\chaptermarkformat}{\chapappifchapterprefix{\nobreakspace}\thechapter\autodot:\enskip}
\let\originaladdchaptertocentry\addchaptertocentry
\renewcommand*{\addchaptertocentry}[2]{%
\IfArgIsEmpty{#1}
{\originaladdchaptertocentry{#1}{#2}}
{\originaladdchaptertocentry{\chapappifchapterprefix{\nobreakspace}#1\autodot}{#2}}%
}
\RedeclareSectionCommand[
tocentrynumberformat={\def\autodot{:}},
tocdynnumwidth
]{chapter}
\begin{document}
\tableofcontents
\chapter{Foo}
\lipsum
\appendix
\chapter{Bar}
\lipsum
\end{document}
Run three times to get

\mychaptercommand? – Vincent Feb 27 '20 at 22:53\mychapter. – esdd Feb 27 '20 at 23:02