Create file/folder permission without delete permission
You cannot disallow deletes and expect rename to work, as explained below.
Windows treats a file renaming operation as a deletion of the file and creation of a new file with the new name. Therefore, you absolutely must have one or both of the following two permissions:
Delete
permission on the file itself, orDelete Subfolders and Files
permission on the folder that contains the file.
To complete the list, for renaming you require in addition the following permissions:
Write Data
permission on the folder because of the new-file creationRead Attributes
permission to both the folder and the actual fileSynchronize
permission to both the folder and the actual fileList Directory
permission to the folder.
These permissions allow the rename command to check for the existence of the file and verify that the file's attributes (for example, the Read Only attribute) don't prevent the rename.
Right click the folder → Properties → Security → Advanced → Permissions → Change Permissions → <select user> → Edit. You can specify (deny) very detailed permissions in there, including the Delete permission
BTW, don't use "CREATOR OWNER" (that was just an example). Use the actual user or group you wish to deny the permission to.
What you write what you want is not possible. If a user wants to rename a file this requires the right to delete it (see Server Fault or WindowsIT Pro).
If it is OK for you that users can create new files in the folder and do with them whatever they want, but not mess with other files (like in a shared temp folder), you can change the permissions for the folder. In Windows Explorer, right click/properties on the folder, Permissions, Advanced, and change permissions. The required rights are:
"this folder, subfolders, files": "Read, Write, Execute" (search folder, list folder, read attributes. read extended attributes, create files, create folders, write attributes, write extended attributes) for the users in question.
"only subfolders and files": full access for "CREATOR OWNER".