From your Stripe dashboard, you can configure payment notifications to be emailed to you directly from Stripe. Just click on your avatar in the top right, then select Profile. Scroll down and you should see a checkbox to enable emails for successful payments.
You can also set up email notifications for disputes, payment reviews, and more here.You can also use your own domain (instead of stripe.com) when sending emails to customers. See Stripe docs for setup instructions.
If Stripe’s built-in payment notifications don’t provide enough customization for you, did you know you can also use Stripe and Zapier to send plain text emails to customers (and custom email notifications to site owners) for Stripe payments? For this and other Zapier examples, check out Stripe + Zapier Integrations That Will Automate Your WP Simple Pay Data.