Microsoft 365 / Office 365 organization name change -- change names or set up new account?

Solution 1:

Once you've logged in through your browser on https://www.office.com with an admin account, you can head to the admin center for any of the tasks you mention:

• you can change the organization's profile (name, address, business details) in https://admin.microsoft.com/AdminPortal/Home#/Settings/OrganizationProfile
• you can add a new domain in https://admin.microsoft.com/Adminportal/Home#/Domains (you can even get rid of the onmicrosoft stuff ..).
• you can then change the access for each user in https://admin.microsoft.com/AdminPortal/Home#/users . You can choose from any domain(s) you have setup in the previous step. You can select multiple users and then select "change domain".

The admin center really is quite straightforward, and you should find anything you need for the migration. In case of troubles, I'd recommend to ask for support directly through the help & support tab in the admin center.

If you have a lot of accounts, I'd ask the suppport if they have a migration assistant available which lets you automate some tasks.