Hmm. You shouldn't have two accounts under a single email.
I would try one or more of the following:
- make sure you choose organization account option when you login to Teams. This is the easiest way usually, but you need to pay attention to which account you are signing into
- login to your personal account and try to add / change the primary alias. It should be possible via Outlook web. Or can you delete the personal account if you can not change the name.
- ask your company admin to change your company account a bit so you end up with different names for accounts
Usually it is not possible to have 1:1 account name & email in both personal and org. This was possible in the history and it caused all kinds of issues..