Hi there @Edward80!
Don here from Shopify. :)
Our Basic Shopify ($29 USD/month) plan does not include domain registration costs, nor do any of our paid plans.
You can learn more about what is included with the Basic Shopify plan (and our other plans) here on our help site.
Not to worry, as you can simply register a domain for a year at a time by purchasing from Shopify directly in your admin or you can purchase a domain from any third-party registrar and connect it to your Shopify account.
Almost all stores we see here would buy a custom domain of some sort to mask the generic 'myshopify.com' URL your store is created with.
If you're just starting out with Shopify, your business might benefit from you checking out the Shopify Academy.
There's a huge amount of learning materials there you can use to learn how to get the most out of your business.
Do you know what you need to work on next for your store or to grow your business?