How can I rename items in the Finder "Places" Sidebar?
They live in ~/Library/Preferences/com.apple.sidebarlists.plist.  The "Places" area corresponds to the useritems key.  If you have XCode (any version) installed you can use the Property List Editor to read and edit that file; otherwise you'll need to use plutil to convert it to XML and back.

I don't know if you can safely rename the entries in that file; they clearly have aliases defined which point back to the originals, but I don't know if the name is ever used for anything other than display or if the Finder will become confused when the alias and name don't match.  Copy the existing one to a backup before playing with it.  You may also need to restart the Finder after editing it or copying the backup back into place:  Option+right click the Finder icon in the Dock and select "Relaunch".