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
You can always use Ctrl + 2 + R
(Press R after appearing a small dropdown) to refactor the variable... [ Got it by chance ].
Update
working on Eclipse Neon... can't say about other older version. because it is the latest stable version at the time I am writing the answer.
Update 3-May-2017
one drawback is that it replaces all occurrences of that variable in the file. special care is required.
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
I noticed that renaming is not available, when the project is not a JS project or if I open it with the non-default JS editor. (Spket JS Editor in my case.)
So try this:
E.g. (In my case I have JS code inside a Java project):
<natures>
<nature>org.eclipse.jdt.core.javanature</nature>
<nature>org.eclipse.wst.jsdt.core.jsNature</nature>
</natures>
Works for my using Eclipse Kepler.