Use BeforeClose...NOT BeforeSave
1 Make endorsed By Blank.
2. Save File using your desired name (The one you are going to send to your users)
3. Save As a different name (eg. Rubbish.xlsm)
4. put a name in endorsed by
5. Exit.
You will now have 2 files. One with a 'proper' name with the 'endorsed by' cell blank. This is what you will give to your users.
Another file with a name in it called 'Rubbish.xlsm', which you can delete
When the users open the file you have given them they won't be able to exit, without having first entered a name in the 'endorsed by' cell.
When they exit, the file will be saved automatically.
I just tried all of those steps with the file you attached, and it worked.
Just as an after thought, you may want to change
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