Is it possible to rename default directories in the users home folder? Can default folders such as Documents, Downloads, Music, etc be renamed to something else? Like how on a Linux system you could edit user-dirs.dirs?

The capitalisation of these direction bugs me as it interferes with my naming convention of everything being lowercase.
Basically you can't. If you mainly work with Terminal you can just set symlinks to make the folders also reachable via the names you are used to (ln -s ~/Documents ~/doc etc). This also works for Finder of course, your home directory may just look a bit cluttered then.