Renaming a Symbolic Link is done from the properties view of the page containing the link. Each link in the list will have a Rename link that will initiate the renaming. The link contains a URL of the form:
http://host/PathToPage?responder=symlink&rename=nameOfLink&newname=newNameForLink


But first we need to create a link to rename.

Included page: CreateRelativeSymbolicLink (edit)

Creating a symbolic link is done in the properties view of the page that will contain the link. There is a form where a user supplies a name for the link and a path for the linked page. When submitted the URL has the following form:

http://host/PathToPage?responder=symlink&linkName=&linkPath=

First we need to create some pages to play with.
Page creator.
Page name. valid?
LinkingPage true
LinkedPage true

Now we create a symbolic link named SymLink. This links LinkedPage as a child of LinkingPage.
Response Requester.
uri status?
LinkingPage?responder=symlink&linkName=SymLink&linkPath=LinkedPage 303


When we look at the properties page we'll see the rename link.
Response Requester.
uri status?
LinkingPage?properties 200
Response Examiner.
type pattern matches? contents?
contents SymLink true
contents <a href="javascript:symbolicLinkRename\(.*\);">Rename</a> true

Now click the Rename link.
Response Requester.
uri status?
LinkingPage?responder=symlink&rename=SymLink&newname=NewLink 303

This should change the name of the symbolic link and redirect back to the properties view.
Response Examiner.
type pattern matches? contents?
contents Location: /LinkingPage\?properties true

When we look at the properties page again, the symbolic link will have a different name.
Response Requester.
uri status?
LinkingPage?properties 200
Response Examiner.
type pattern matches?
contents NewLink true
contents SymLink false