Hi Sabcat,

I understand you’d like to add your domain located at UK2 at Office 365.

Generally, you can refer to the following steps:

1, Add your domain name at Office 365.
Log into Office 365 portal, click Admin on the top; click Domains on the left panel; click Add a domain; type your domain name; click Next.

2, Follow the steps in the wizard to verify with Office 365 that the domain name you have added belongs to you. For step-by-step directions, please refer to Verify a domain at any domain name registrar.
Tip: If you can’t find your domain registrar listed in the guide, please follow the general instruction.

3, Update your domain’s name server records.
When completing the Add a domain wizard, click Change name server. Otherwise, see Change name server records at a domain registrar.

4, Update your SharePoint website address to use your own domain.
Log into Office 365 portal, click Admin on the top; click Domains on the left panel; beside “Your SharePoint website address”, click Change address; follow the guide to update your SharePoint website address.
Tip: This change may take up to 24 hours to complete.

For more information, you can refer to the following articles:
Add a new domain to Office 365
Troubleshoot domain verification issues in Office 365

If you need any further assistance, pleas feel free to post back.

Thanks,
Evan Zhang