Great question about domain names. We would be happy to assist you with changing the primary domain name on your hosting account. Please review our article How do I change the primary domain on my account? for the steps to take and important information to keep in mind when changing your primary domain name.
Thanks for the question! You will need to first change your domain name in WordPress. We have a tutorial called Changing your WordPress URL. Follow the tutorial and any post made after the change will be using the new domain name. You will need to park your old domain name so that anyone going to the old domain will be redirected to the new one.
I hope that helps to answer your question! Let us know if you require any further assistance.