This is an accepted solution.
Hank here from Shopify.
When you create an account with Shopify initially you are automatically assigned a free “myshopify.com” domain, which is then used as a unique identifier for your store and is therefore not subject to change. It’s best to think of it as similar to a bank account number, we need it to find your account in our servers for all operations so it cannot be duplicated. However, what we do encourage is that you explore the idea of purchasing a custom domain either through Shopify, or you can purchase one from a third-party provider.
This may have been the step that you mentioned you took, which means you have a customer-facing custom domain that you can set as your primary domain. It helps establish your brand and helps separate you from the platform that powers your website, which is Shopify.
So while you are able to change your store name in your admin (Settings > General) you wouldn’t be able to change the “.myshopify.com” URL once it has been created but as I mentioned, you can cover this with a custom domain so that the only people to see the “.myshopify.com” URL will be those logged into the admin.
Let me know if you have any additional questions!
All the best,