Two identical accounts on Office365

I have 2 identical Office365 accounts that are mixed by Office 365:

On acquiring Office365 Home I registered the Office 365 account using the email adres "email address removed for privacy reasons"

The serviceprovider that hosted my domain and email then migrated its service to Office365, using the same accountname.

I now have two Office 365 accounts with the same name:

1) The private made "myname@mydomainname" Office Home account with Office 365

2) The "myname@mydomainname" email account of the service provider ("school / work account")

On selecting the account I sometimes can select "private made account" or the "school / work" account. However, e.g. on wanting to install Office it always uses the account of te service provider and gives no choice to select the Office Home account....

How can I solve this ??

Thanks,

Marc