Changing the custom and redirecting domain on an existing shopify account

[Flow13]

I have an existing primary domain on Shopify and store as well as a 3rd party domain it routes to.

I'm changing the name of the business and would like to change the primary domain at Shopify, as well as add a new domain name I've purchased.

BUT, I'd like the site the remain the same - the template, setup, all the items for sale, etc.  Just need to change the two domains.  What's the easiest way to do that?

Thanks so much for any help! 🤗