That's incorrect -- the absolute path in Unix (BSD) is '/' (root) -- for the boot drive (you're right that all other drives mount to /Volumes/[Device Name]). The name (e.g., Macintosh HDD) is fairly meaningless as even the mount is done by Unix device (usually /dev/disk1).No, see above.
Once the OS is up, have you tried to simply click on the drive once, hit "Enter" and rename? What happens when you try a couple of letters -- say, "abc"?
Alternately, if you boot into recovery -- Command (⌘) + R -- right after the Apple 'gong' sound, you should be able to go into Disk Utility and rename the drive.