Setting up an Exchange Server 2007

I have a domain that is hosted by EarthLink. This is where i go to control our Web Page and Company’s email. I want to take our companies email and put it on an Exchange Server. The question is that our External Domain name and our Internal Domain name is different. Do i have to change my internal domain name to match our external one? Exchange Server runs off of Active Directory right? I am confused on how all of that works. Any help would be great. Thanks