From FCKeditor Docs

RenameFile

Renames a file.

Sample Request

In the root directory of the resource type “Files”, rename the file “My File.jpg” to “New Name.jpg”.

connector.php?command=RenameFile&type=Files&currentFolder=%2F&fileName=My%20File.jpg&newFileName=New%20Name.jpg

Sample Response

<?xml version="1.0" encoding="utf-8"?>
<Connector resourceType="Files">
 <Error number="0" />
 <CurrentFolder path="/" url="/userfiles/files/" acl="255" />
 <RenamedFile name="My File.jpg" newName="New Name.jpg" />
</Connector>

Note that the file names may contain non ASC-II chars.