In Eclipse (I am running 3.8.0 @ Linux (Mint 14 (Ubuntu (Debian))) at the moment), renaming variables using Refactor is an option that seems random
Eclipse
Refactor
I can rename the local variable under Aptana Studio 3.0 (Eclipse based) with the JSDT "JavaScript Editor" and in the screenshot shown JS function: http://imgur.com/246oTY5