Hey @kgawron .
Thanks for reaching out.
You can purchase a domain directly from the Shopify store by navigating to Domains > Buy New Domain to add your own custom domain. With that being said, you are unable to make changes to the checkout URL when customers navigate to complete their purchase unless you are using the Shopify Plus subscription. However, I can certainly see the benefit creating a unique checkout URL for your customers to complete their purchase - I am going to provide this as a suggestion to our developers. We appreciate you reaching out with this feedback as this is how we can improve the platform for all merchants.
Let us know if you have any questions.