How do I change the wpstaging.com domain to new domain without damaging the website?

I've created a website with Wordpress and the site is under a wpstaging.com domain at the moment. I have my main domain name and hosting with an external hosting company - nothing has be set up on that yet.

I would like to find out how to go about changing the wpstaging.com domain name to the one I've got with the hosting company and moving the website over to the new domain name without damaging the current website.