When you go into the domain settings (Admin > Settings > Domains), under the myshopify.com URL, there should be a link for “change to a new myshopify.com domain” which you can click to change to a different handle.
However, if you add a custom domain name (ex. yourstore.com), the custom domain will replace the myshopify.com URL, so customers will only see your custom domain name … so it doesn’t really matter what the myshopify.com URL is.
With regards to the sender email address – you can edit this from your notifications settings (admin > settings > notifications).
It’s best to use a professional email address for this, which you can usually purchase via your domain provider (if you didn’t buy the domain via Shopify). I recommend using GoDaddy for purchasing professional email addresses (https://www.godaddy.com/en-ca/email/professional-business-email). Once you’ve purchased a professional email address, and added it to the ‘notifications’ settings on Shopify, you’ll need to add some DNS records so that Shopify can send emails from this address. You’ll see some instructions on the ‘notifications’ settings page for what those records need to be.
You’ll also want to set up a DMARC text record for your domain. I’ve posted instructions for setting up a DMARC record on this thread: https://community.shopify.com/post/2369290