Remove additional mailbox from being displayed in Outlook client

2 ways to remove the leftover name on your screen, after the mailbox is closed.
    ( It will not go away after removing it from the open additional mailboxes tab )

# 1 -
Connect to Exchange Online by using remote PowerShell.
Remove full access permissions for the user from the mailbox. This removes automapping. To do this,
at the command prompt, type the following command, and then press Enter:
Remove-MailboxPermission -Identity <Mailbox ID1> -User <Mailbox ID2> -AccessRights FullAccess
Here is an example with a valid user-
Remove-MailboxPermission -Identity -User -AccessRights FullAccess
# 2 -
ADSIEdit.msc, Domain context, and drill down to the account you wish to be removed from, and look for the 
"MSExchDelegateListLink" attribute and remove yourself from that list.  The next time you start Outlook 2010, 
the ghost "additional" mailbox should disappear after a few minutes.
If you go to the location in Outlook to Add addition mailboxes, and add one, it seems that you see the rest.  Doesn't help with removing the one you no long have access to.  So, it's hard to say if it's one bug or two, the mailboxPermission PS command exchange uses, doesn't seem to check/clear the MSExchDelegateListLink attribute, and possibly another bug with Outlook not actually listing "Addition Mailboxes" unless you add one, then you see many.
You can still re-add the same mailbox after clearing the adsiedit entry.
There is no specific clients and service packs that this impacts.
The feature mailbox automapping.