You can rename Macintosh HD, but there are some side-effects
You can rename Macintosh HD, by (a) selecting it, clicking once in the name, and then typing, or (b) selecting it, clicking command-I (or doing File, Get Info), and then typing.
Most things continue to work fine, (I have runs Macs for years with Macintosh HD renamed). However you may experience some side effects, and new releases of Mac OS X or applications may cause new ones. Side effects I have encountered are:
(1) MS Office 2011, and probably older versions too, cannot handle valid Mac OS X file names, so if you rename it to "27" iMac HD", MS Word cannot open its template Normal.dotm, and generally gets in a mess. I had to make the name "27 inch iMac HD".
(2) When you connect to the Mac from another computer on the network to share files, instead of seeing the new name, you will still see "Macintosh HD." This is annoying, as the reason I changed the name in the first place was so that it would be obvious on other computers when they were accessing the hard drive of a different computer and not their own drive.
(3) Any stored pathnames including "Macintosh HD" could potentially have problems, however, the persistence of "Macintosh HD" (I think this is the "short name"), noted in (2) above, means that in most or all cases, this will not be a problem.
(4) I have seen, but not experienced, problems such as reported here: "when I do this, it won't let me open some programs or even go into the desktop and screensave preference pane.... any ideas?"
I suggest you change it, but suspect it as a possible cause of any problems you experience over the next few weeks; just temporarily change it back to Macintosh HD to see if that makes the problem go away.
Good luck!