It's pretty easy to do, but you don't have to actually create an additional e-mail address for that.
1. Make sure that your DNS Provider has the MX record for the new domain pointing to your public address of your Exchange server. I doubt you are running your OWN public DNS servers - so you may need your Internet Providers assistance for this.
2. On the Exchange Server - use Exchange System Manager to navigate Recipients | Recipient Policies | Default Policy and add the domain @domain2.com (replace domain2.com with the actual domain) to the list. This will allow your Exchange server to accept mail for this domain
3. Make sure that your user in Active Directory Users and Computers has the address
name@domain2.com on it