The "on behalf of" is text that is specific to Outlook and it displays based on the Internet Headers of the email message that is received. It's looking at the sender and comparing it with the Reply-To header. Here's an example:

Sender: organization <>
Reply-To: John Doe <>

In this case, Outlook knows that the true sender is, but it sees something else in the Reply-To header and infers that the email is being sent by on behalf of John Doe.