Change primary email address in Office 365

Start powershell as administrator

Run the following commands:
$LiveCred = Get-Credential
(Enter your Office 365 administrator credentials)
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection
Import-PSSession $Session

Find all aliases for one account:
get-mailbox | select -expand emailaddresses alias
Alternativt:
get-mailbox name@domain.com | select -expand emailaddresses alias

Add email alias to an Account:
Set-Mailbox name@domain.com -EmailAddresses SMTP:newprimaryaddress@domain.com,anotheraddress@domain.com,yet.another.address@domain.com

NOTE: the first address after “SMTP:” will be the primary e-mail address. All aliases will be replaced. If you have 100 aliases and only type in one in this command, you will lose 99 aliases!