Cal here from Shopify, thanks for reaching out to us. Are you referring to your MyShopify URL? Once you open your store, and choose your MyShopify URL, this cannot be altered.
The MyShopify URL is largely used for login and support services, and most businesses would look to purchase their own domain for their store when they are ready to launch. If you purchase a domain and make it your primary domain, your customers will never see your MyShopify URL.
If you'd like to learn more about purchasing a domain you can read our article on this here.
Let me know if you have any other questions, I'd be happy to assist!