The email address you use for your Shopify store is up to you. You can use a @shopify.com email address, or you can set up your own custom email address using a domain name that you own.
If you want to use a @shopify.com email address, you can create one from yourShopifyDomain.myshopify.com/admin/settings/general page.
If you want to use a custom email address, you need to set up email forwarding from your domain's DNS settings. For more information on setting up email forwarding, please see this guide from Shopify.