You may have several email addresses to choose from for putting on your business cards. Each person with an Engineering account will have an email address of 'mylogin@ENGR.ORST.EDU'. (Of course, replace 'mylogin' with your login name.) Currently Engineering also receives mail for:
So, if you want to have your email address reflect your department, you could just as easily announce your email address as 'mylogin@ME.ORST.EDU' as 'mylogin@ENGR.ORST.EDU'.
You can also use an email address of 'First.Last@orst.edu' if you are a staff or faculty member. This will need to be setup on a case-by-case basis. This mail can be sent to either the exchange server or any other email address that you want.
You can publicize whatever email address suits you. None of those names should go away anytime soon. Some may be more appropriate than others.
Do not publicize specific machine names such as 'firstname.lastname@example.org'.