In a situation like you describe, there are 2 fields to deal with. The PRINCIPAL field will contain the name of the generic mailbox; the FROM field will contain the name of the person that actually did the sending.
It’s true that the “Customize this view” menu option doesn’t provide the ability to make the change you’d like. However, you could use the Designer do what you want.
To search for mail sent by a particular person, just search for PRINCIPAL=username OR FROM=username