You can cehck the manual here https://help.shopify.com/manual/domains
Koreen here from the Guru Team at Shopify. Thanks for posting. :)
I'd just like to chime in a little here. The .myshopify domain will always remain with your store and cannot be edited or removed. However, once you have your custom set up, you can then use this to completely cover this Shopify domain, so it will not be in any way public facing.
Generally once you purchase a custom domain through Shopify, you should see this in the domain section of your admin.
These work as a third party domain, however the the difference is that we help set this process up for you. :)
This it can take a little while for it to propagate fully, however as soon as you see the green beside your domain, you can then select this to be your primary domain.
This is then the domain that will show in the URL when your customers search for or arrive to your store.
I hope this helps!