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Explanation
For Office365 you can use any domain, regardless of where it is registered. You only need access to the DNS zone of the domain, because you have to make settings there.
Configure your own domain
Please log in to the admin panel of Office365 to configure your domain:
Then navigate on the left side to "Show all" -> "Setup" -> "Domains":
Now click on "Add domain" and follow the instructions listed there.