Hi Arun,
Move, rename and edit operations come under modification of the page, so you must select modify checkbox. We don't have separate permissions only for the move and rename and separate permissions for only editing the content all come under Modify and create permission
Please refer below article for the list of permissions:
https://experienceleague.adobe.com/docs/experience-manager-64/administering/security/security.html?l...
Usually, the publisher will publish the page, if he sees any issues he must redirect to content authors for modification's.