An issue came up in the past where outlook showed on behalf of for the sender. Other services, like gmail did not.
Generally this means the sender and from address to not match. In this particular case PHPlist was used, and phpmail was used not setting the sender. In the headers there was a sender header:
Sender: <[email protected]>
the from was From: <[email protected]>
Using SMTP over php mail was the fix. Setting the sender with -f in php mail can be used as well, but this varies based on the script in use.
Mailbaby recommends setting DKIM for your domain name in your mailing software or control panel.