Since XWIKI-3398 , Rename checks for delete rights.
For document creators
$xwiki.hasAccessLevel('delete') returns 'false' (used by rename.vm)
$xwiki.checkAccess($doc.fullName, 'delete') returns 'true' (used by menuview.vm).
Normally document creators have 'delete' right and should be able to rename the page, especially since they can delete it.
Selecting 'rename' retuns 'You are not allowed to view this document or perform this action.'