The tenant is your Office 365 account, including hosted Exchange, Skype for Business, SharePoint, and your Office 365 Active Directory. The first account that you create when you first purchase Office 365 is the "owner" of your tenant. This account should be an admin account, not a person. This account does not normally require an Office 365 license. Relating to SharePoint, all of your site collections are within your tenant. You can have any number of domains within your tenant (with e-mail accounts), but you will have only one root SharePoint URL:https://xxxx.sharepoint.com.
The Global Administrator account is similar to the Company administrator. Users in this role have access to everything or the permission to add them to a dedicated role where they do not have permission (such as discovery management and assigning administrative roles to other users).
When setting up Office 365 the first step is to purchase your subscription which includes choosing the plan. Step 2 involves the selection of the sign-on method and this is where the global administrator account is of consequence. Step 3 involves the collecting of information such as domain names and DNS, locations, etc
Step4 is the actual migration plan and schedule, step 5 the Microsoft account and organizational account, step 6 the SkyDrive and SkyDrive Pro, and step 7 the Windows Intune section.
Thus you should perform step 1 through 3 to ensure that all user accounts to make use of a custom domain for their e-mail.
References:
Katzer, Matthew and Don Crawford, Office 365 Migrating and Managing your Business in the Cloud, Apress Media, New York, 2013, pp 87- 93, 373 http://office.microsoft.com/en-gb/office365-suite-help/add-your-domain-to-office-365-HA102818660.aspx
