You can rename project-root inside the tarball with the 7-zip GUI (and probably other archiver programs as well), but this may do a full decompression-recompression cycle on compressed tarballs. (Read: this may take a while on large, heavily-compressed tarballs.)
The best way to do what you want is to change the name before creating the tarball. A simple way would be to temporarily rename project-root to something-else:
# temporary rename; tar; restore original name
$ mv project-root something-else ; tar cjf foo.tar.bz2 something-else ; mv something-else project-root
I'd probably go a little more complicated: make a copy with the name I want in the tarball. This avoids potential bugs or missed steps in whatever fix-it-up-later process might be employed, and I might want to keep both copies around for other purposes.
# make me a copy
$ ( cd project-root ; tar cf - . ) | ( mkdir something-else; cd something-else; tar xf - )
# test the copy here if needed
$ diff -r --brief project-root/ something-else/
# create my tarball
$ tar cjf foo.tar.bz2 something-else
tar's scope (which is why there's no option for it). generally if you have a project and want to make a point release, you'd use your version control tools to set certain versions of certain files as project v0.1, or v0.2, etc. then checkout the v0.1 files to a new directory project-0.1, tar that directory, and tahdaaaah, done. – quack quixote Jan 20 '10 at 2:44