Rename symlinks linking to ~/Documents It is not possible to rename symlinks to one default folders in your home folder (~/Documents, ~/Desktop etc...) using Finder
This works in Terminal.

Update 2

To test:


run ln -s Documents "Documents symlink" in terminal.
verify you can't rename ~/Documents symlink in Finder
verify that running mv "Documents symlink" "Document symlink new" works
I've started using an application called DTerm in the last few weeks, and it could help to make this task relatively painless.

The point of DTerm is to provide a command line specific to where you are, and with context to the application you're in. While you're in the Finder, DTerm provides a command line in the current folder in the front-most/active window you're viewing.

I have an Applications folder in my Home Folder, and a symlink called bin pointing to it for compatibility's-sake.



Note how the folder icon carries the standard Applications icon, but has the shortcut arrow.

By invoking DTerm using a configured keyboard shortcut, I can immediately rename that folder.



There's three things going on here:


The input field which I've typed the command into.
The command line is expanded/returned for things like variables and globbing (using the * for matching files).
The empty field under the returned command is a static text field for output/errors. Neither of which occur when using the mv command, at least not in my invocation.


And then of course, I rename it back:



Best of all? DTerm is available completely free of charge. The link at the top of this post will take you to the author's website, and here is a DTerm Mac App Store Link.