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Thanks for posting here.
I understand that you would like to sign in to the Office 365 portal and SharePoint Online with the sign-in address: firstname.lastname@example.org instead of the original one: email@example.com. Is it right?
If it is the case, it needs to add your custom domain to Office 365 successfully and then change user’s address in the Microsoft Online Portal (MOP). If you are on the process of transition from OLSB to Office 365, you may refer to this article remove your domain from OLSB to Office 365:
In addition, to change user’s sign-in address, please firstly log in to MOP with an administrator account and password, and then click Users in the left panel of the home page. Then locate the user you need to change address, click Details, and change user name as in the following example:
If there is any misunderstanding, please feel free to correct me in the forum.
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