Hi @lltlawservices,
By default, the customer received an email after confirming their order. Although, that email does not has the vendor address.
However, adding additional content and vendor address inside the customer order email requires customization of the WooCommerce default email template. You will need to override the template and customize the email template as per your requirement.
Basically, there are three email templates by default by which WooCommerce manage the customer order emails.
You will find the email template in the below file path:
woocommerce/templates/emails/customer-on-hold-order.php
woocommerce/templates/emails/customer-processing-order.php
woocommerce/templates/emails/customer-completed-order.php
I hope the information will help.
Best Regards!