How does one change the share name with file sharing in Mac OS X?
Use Directory Utility.


Open /System/Library/CoreServices/Applications/Directory Utility
Select the Directory Editor tab
In the "Viewing" bar, select SharePoints in node /Local/Default
Authenticate by clicking the little lock button


Shares are listed in the left-hand column. Select one and update the following as needed: 


RecordName (the name of the listing)
dsAttrTypeNative:smb_name
dsAttrTypeNative:afp_name


Changes should take effect immediately.

Apple hid this utility for a reason: Be careful, a wrong Directory entry can wreck your Mac. 

Renaming sharepoints used to be possible with the Server app, but filesharing is now handled by the normal MacOS System Preference pane.