There are several administrator roles available in Office 365, like the billing administrator, password administrator, service administrator, and user management administrator, but the most important one will probably be the global administrator. The reason for this is because it is the only administrator account that is able to assign other accounts administrator roles.

The account signing up for a new Office 365 subscription will automatically be assigned the Global Administrator role. After signing up, you are free to have more than one global administrator.

In order to assign the global administrator role to an active user, follow the steps below:

1. Go to http://portal.office.com and log in as a global administrator.
2. Go to the Office 365 admin center site.
3. Click the USERS link in the left navigation and choose Active Users.
4. In the list of Active Users, locate the user you wish to assign the global administrator role to and check the checkbox next to it.
5. Click the EDIT link to the right below the avatar for the user.
6. In the left navigation choose the link Settings.
7. In the section called Assign role, choose the radio button Yes and select Global administrator in the dropdown menu.
8. Provide and alternate email address for the user.
9. Hit the Save button at the bottom of the page.

In order to find the all users who have been assigned the global administrator role, you can use the following Windows Powershell.

(Please note that you need to install Microsoft Online Service Sign-in Assistant for IT Professionals RTW first and afterwards Azure Active Directory Module for Windows PowerShell (64-bit version) on the system you are running the script from. Otherwise it will not work.)

$credentials = Get-Credential
Import-Module MsOnline
Connect-MsolService -Credential $credentials
$companyAdministratorRole = Get-MsolRole -RoleName "Company Administrator"
Get-MsolRoleMember -RoleObjectId $companyAdministratorRole.ObjectId

The Office 365 tenant name is an important subject to cover before diving deep into the Office 365 world. I would therefore like to take the opportunity to explain what it is, its limitations, and how it works.

When you sign up for an Office 365 subscription, you are asked to provide a domain name which will be your tenant name and used for .onmicrosoft.com. At this point you will have to consider this choice carefully, since you will be unable to change this at a later time. If you want to change the tenant name, you will need to sign up for a new subscription again with a new tenant name.

If you plan to use your trial tenant for production, be sure to choose a name for the tenant that is different from your planned production tenant name. It’s a common mistake to use a company name for the trial. The name of the tenant appears in Lync invites and SharePoint Online, but Microsoft does not currently have tools to rename a tenant or migrate data from one tenant to another. If you change your mind later, you have to create a new tenant and manually move your data and settings. (https://technet.microsoft.com/en-us/library/hh852435.aspx)

The tenant name will be under onmicrosoft.com, which is globally signed. This means that if a company in Europe has already signed up for a domain name called ex. foobar.onmicrosoft.com where the tenant name is foobar, then a company in Asia will be unable  to sign up for the same domain name. This limitation has not always been true. Under the predecessor Business Productivity Online Standard Suite (BPOS), which was the previous name and version of Office 365, the subscriptions was divided into three regions called microsoftonline.com, emea.microsoftonline.com, and apac.microsoftonline.com. But now we only have onmicrosoft.com available in Office 365.

Another important point to consider when choosing the tenant name, is that it will be a part of your SharePoint URL which comes with the Office 365 subscription. Ex. http://yourtenantname.sharepoint.com.

If you want to check whether a tenant name is available for a new Office 365 subscription, I will recommend using the following website: http://office365check.azurewebsites.net.