I don't run an open relay, so there is a little more configuration to ensure safe communication.
If you would like to have Gmail send email through your web server and not have that annoying "on behalf of", here is how to do it:
1) Click on Options in the Top Right corner
2) Select Settings
3) Click on the Accounts tab
4) Click Edit Info for the account you want to edit
5) Enter your name as you want it displayed
6) Select “Send through YOURDOMAINHERE SMTP server.
Enter your SMTP server (smtp.YOURDOMAINNAMEHERE.com).
Select “Secured connection using SSL”
Enter Port 465
Your email will now be sent from Gmail through your server with no traces of Gmail for the average user.