You may be able to carefully re-name a hard disk drive with OS X system on board by
use of the OS X Recovery's version of OS X Utilities, where you may be able to also
and secondarily (if desired) erase and reformat. However you'd not want to go that far.
• OS X Mavericks: Rename items on your Mac
Part of the problem in re-naming a hard drive, may be the computer name is also used
by other processes, & additionally that name is shared with other computers networked.
See many replies to search of topic, using words 'how to rename hard drive on Mac OS X'
https://duckduckgo.com/?q=How+to+rename+hard+drive+on+Mac+OS+X&t=ffsb
{Some are not valid, or may go to questionable sites due to too many 'fake choice' click-ons.}
Of those, some point back to support discussions; others pertain to different OS X versions
and some cover details under differing circumstances that may or may not be similar to the
underlying issue behind a problem you see. Different causes may result in similar symptom.
Do you have a TimeMachine backup of your computer drive on an external storage? An
improperly named or re-named hard drive in the Mac may not see or accept an old TM
backup if the names differ. See the name Pondini among Apple support searches as he
provided some great advice, for a limited time, and some of that wisdom is still online.
Good luck & happy computing! 🙂