Dear Peter E69
Thank you for your reply!
Can you check if your gmail.com has all the content under your email account? I think your email content might be in Gmail and not Outlook.
Typically this problem only occurs if you have registered a Microsoft account using an email account with a non-Microsoft domain. In principle, it should be the case that the problem occurs when the primary alias of your Microsoft account is a non-Microsoft account. Each Microsoft account is automatically generated when it is created with an outlook email name with the numbers and letters you see at the beginning of outlook. As I mentioned in my first reply, Outlook.com does not accept logins from non-Microsoft email addresses. That means it will not show your gmail name in outlook.com. It will definitely show a Microsoft domain email name. So this auto-generated strange mailbox will show up. That's where this strange mailbox name comes from.
You mentioned that you have multiple mailboxes configured in Outlook, so I guess you're using the desktop version of outlook (New Outlook or Outlook classic). Both of these applications are supporting the configuration of non-Microsoft email accounts. This means that Gmail email accounts are also allowed to log in to your Outlook desktop version. At this point your gmail name will have two meanings, there will be two mailboxes (a Gmail account and a Microsoft account) corresponding to this name, and by default Outlook desktop version will think that this is a Gmail account and not a Microsoft mailbox account. So I think your mailbox data may be stored in Gmail, I suggest you visit the web version of Gmail to see if you can see the correct mailbox content.
In order to correctly distinguish between a mailbox name corresponding to two mailboxes, I think a better solution would be to create a Microsoft domain alias for your Microsoft email account. No need to delete the original gmail alias,You can log in directly using the newly created alias.
If you hold a Microsoft 365 subscription, I would more than recommend that you do so. If you use a Gmail name, there may be some issues with subscription benefits not working properly. (e.g. exempt adverts in New Outlook)
I hope that my reply has been helpful to you! If you have any other questions, reply to me at the bottom of this post at any time!
I wish you all the best
Carmid.L-MSFT | Microsoft Community Support Specialist