You got me confused with the reference to nullmailer … Checkmk itself does not include nullmailer or any other MTA, it just uses mail (heirloom-mailx) as a client to talk to the local MTA (nullmailer in the appliance, postfix in your case).
In your notification rules, you can set the From address and display name for the outgoing notification mails.
Or you could set up an address mapping in your local postfix, see Postfix Address Rewriting