When you purchase a new domain, several steps will need to be performed before being able to use it within Office 365.
In order to add a domain, you must have access to modify your domain's DNS zone.
Contact CDS Customer Care to request the domain be added to Office 365, Proofpoint, and CloudPortal Services Manager (CPSM). We will respond with a TXT record you must add to DNS in order to verify the domain in Office 365.
You will now need to configure DNS for the new domain to work with Proofpoint and Office 365. Please refer to the Exchange Online DNS guide and the Skype for Business Online DNS guide for information on the necessary entries.
When you have received confirmation that the domain is added to CPSM, you will need to restart AD Sync on all of your domain controllers for them to recognize the new domain. Restarting AD Sync allows the service to download the latest configuration data for your tenant account. This includes the list of domains available to synchronize with CPSM. Failure to restart AD Sync will result in errors when trying to add users to the AD Sync group that use this domain.