I have a user who has created a site with custom permissions. These permissions are basically contribute but without the delete action on list items. The users who have this permission level attached to their account have said they cannot rename folders. Would someone be able to tell me if this is normal SharePoint behaviour?
This behavior is by design.
This behavior corresponds to user's experience on Windows file servers or when users access to a SharePoint web server through Explorer View (WebDAV HTTP protocol extension).
Here is the MSFT KB Article on this issue.
The user must have delete permissions to rename files/folders.