I am trying to make my chapter titles show in the document's header. I know of the \rightmark and \leftmark commands, but I wish to customize the look of the header while still showing the chapter titles. This is what I currently have. It only produces "Chapter [number]: Chapter" on every page.

\usepackage{fancyhdr}
\pagestyle{fancy}

\fancyfoot{}
\fancyfoot[LE,RO]{\thepage}
\fancyfoot[CO,RE]{name}


Your question is not very clear but I guess you want something like this:

\documentclass{book}

\usepackage{blindtext} % <================= dummy text or dummy document

\usepackage{fancyhdr}
\pagestyle{fancy}
%\renewcommand{\chaptermark}[1]{%
%\markboth{\chaptername\ \thechapter.\ #1}{}% <============== standard
%}
\renewcommand{\chaptermark}[1]{%
\markboth{\chaptername\ \thechapter.\ \textit{#1}}{}%
}

\fancyfoot{}
\fancyfoot[LE,RO]{\thepage}
\fancyfoot[CO,RE]{name}

\begin{document}
\Blinddocument
\end{document}


With package blindtext you can generate a dummy text or document to have a look on the generated header and footer.

To get for example an italic title of chapter in the header you can redefine the \chaptermark like

\markboth{\chaptername\ \thechapter.\ \textit{#1}}{}


That means you get the text Chapter (content of chaptername), blank, chapter number (\thecapter), dot, blank, chapter titel in italic (\textit{#1}).

Please see I changed CO to LO to get the \leftmark printed left (L) instead centered (C)! Looks better imho.

With the given mwe you get the result: