How do I change the domain name of my AD DS? [closed]

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http://serverfault.com – I recently set up a server with AD DC and used a mydomain.local address for it. I now would like to be able to access the server through remote desktop from outside my local network. So I have purchased a domain name that I have set up with my router for DDNS and forwarded to the IP of my server. I was wondering a few things. A) Is there a way I can forward the DDNS to point to my current AD DC x.local address so I wouldn't have to change the domain to log in from outside of local network? B) If there is not a way to do what I mentioned above, what is the easiest way to change the Domain Nam (HowTos)