By default when Exchange Online in Office 365 is setup for your organization, the postmaster address, e.g. firstname.lastname@example.org is set to email@example.com.
This means that when someone sends mail to your organization and gets an NDR back, the sender is: firstname.lastname@example.org.
If you want to change this, you can do so using PowerShell for Exchange Online.
The procedure for changing this is:
1. Connect to your Exchange online using PowerShell
2. Change addres using command:
Set-TransportConfig –ExternalPostmasterAddress email@example.com
This works for All P and E plans – I have not tested it yet for K plan.
This postmaster address is a tenant/organization level setting which applies to all domains in your tenant. It is not available to set the postmaster address on a domain level.