Adding a custom domain or updating your .myshopify.com URL will only update what your customers see when they visit your storefront. The original .myshopify.com URL you got when you first created your store will still be the domain displayed in your Shopify admin URL. Your original .myshopify.com domain will also still be the domain you use to log in to your store, and the domain Shopify Support uses to identify your account. Since this is expected behaviour, there isn't a way to change this. That being said, I can share your feedback about this with our team who reviews improvements we can make to the platform.
Please let me know if you have any questions! The following guides may be able to help as well: