I am not aware of any built-in facility of the book class,
or any of the other standard classes, that automatically
assigns a "chapter title" (or book title) which can thereafter
be used in, e.g., a header. Certainly when one begins a
section with, e.g.,
\section{The Art and Science of Constructing MWEs},
nothing (that I know of) automatically stores
the string "The Art and Science of Constructing MWEs".
So (unless there is already a package out there to do
this and more) you will in any case have to have some
"syntax written down" for storing that string, then
recovering it for use in your header. (Actually,
it occurs to me that the required information *is* being
stored for use in the table of contents--but it is not
clear to me that extracting it from there would be worth
the trouble.)
My solution to a similar problem (similar but not identical
because (1) I was using memoir.cls rather than book.cls, and
memoir.cls incorporates features of fancyhdr--you might,
in fact, want to switch from book to memoir, for that and
many other reasons, and (2) I wanted the chapter name,
or rather a running head that might be a shortened version
of the chapter name, not a section name, on odd-numbered
pages [except of course the first page of the chapter,
which for my set-up was always odd-numbered; presumably
your sections can start on either even or odd pages, and
may even start in the middle of a page {meaning that you
must give some thought to the header on such a page}, and
the chapter author[s], not the book title, on even-numbered
pages) was as follows. In my preamble I defined
\def\subhead#1{\def\subheadcontents{#1}}
\def\subauthor#1{\def\subauthorname{#1}}
then initialized
\def\subheadcontents{\relax}
\def\subauthorname{\relax}
and proclaimed
\pagestyle{myheadings}
\makeevenhead{myheadings}{\thepage\qquad\subauthorname}{}{}
\makeoddhead{myheadings}{}{}{\subheadcontents\quad\thepage}
(in fact, it turned out to be somewhat different, because
when I was nearly done with the book, my publisher belatedly
informed me that the house style for chapters was to have
all major words [i.e., exclusing non-initial digraphs, "and",
etc.] capitalized *on the title page of the chapter and in
the table of contents*, but only the first word [and
proper nouns, and the first word following an internal
colon or em-dash...] capitalized *in the running head*,
grrrh). Then at the beginning of a chapter I could
write
\subhead{The Art and Science of Constructing MWEs}%
\subauthor{F. X. Spezial}%
\chapter{\subcontentsname\label{chap:\subcontentsname}}
and it all worked. (Maybe it shouldn't have; I don't
claim my way was "the right way", or even merely that
my way was right--I might have just been lucky. And
certainly, if I had been serious, I would have
automatically accomodated the few cases--in the
actual book in question--when I had to tweak the
chapter title in the table of contents [for esthetic
reasons] or abbreviate the chapter title in the
header [because it was too long altogether].)
Something along those lines might work for you. Or,
if you don't want to automate anything at all,
just start each chapter with the appropriate
handcrafted variation of the fancyhdr-like-syntax
given above (beginning with "\pagestyle{" and ending
with "\thepage}").
Lee Rudolph