If you want to let external user rename files or move files in the document library, you need to share the entire site with external user not only a file. Here are steps:
1.Go to the site -> Site settings -> Site permissions -> Add members -> Share site only.
2.Enter the external user account.
3.External user can access the site through email invitation link, then rename files or move files in the document library.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.