For a more professional appearance and full SEO potential, your store should not run on the Shopify subdomain but on its own domain.
You can buy your custom domain name at several domain registrars. For example, at godadddy.com or namecheap.com. After you purchase a domain from a third-party domain provider, you need to connect your domain to your Shopify store. Connecting your domain points your URL to your Shopify store so that customers can enter that URL into their web browser to visit your online store.