@Kyuzo88, Thanks for posting in Q&A. Based on my test, the "Other user" option will not hide when we configure shared multi-user profile. The same result as yours. I think this is by design.
Then I go to do some researching and test on some registry key like below
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Policies\System]
"dontdisplaylastusername"=dword:00000001
But it is not working. You can contact windows support to see if there's any method can disable the "Other user" option.
Thanks for your understanding.
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