Quoting Stephane Chazelas from this answer on Unix & Linux SE.
To rename a file, write permissions to the file don't matter, renaming
a file is a change to the directory, not the file. That's changing the
directory entry to have a different name pointing to the file.
So all you need to do is change the permissions of the directory. For
chown root: .
chmod 755 .
That will prevent users from renaming files in there, but also from
creating or deleting files. If you still want them to be able to do
that, you could instead make the directory writeable but also set the
t bit. With that bit set, users (other than the owner of the
directory who is not restricted) can only delete or rename the files
chown root:people-who-can-create-file-here .
chmod 1775 .
chown root:people-who-can-modify-the-files file1-that-must-not-be-rename ...
chmod 664 file1-that-must-not-be-rename ...