Does Shopify offer an email address with my account?
Shopify does not provide email hosting.
Contact forms, etcs will be sent to the store owners email or staff for some notifications.
If you have a domain through shopify there is email forwarding
Read the manual https://help.shopify.com/en/manual/domains/email-forwarding-and-hosting/email-hosting
https://help.shopify.com/en/manual/intro-to-shopify/initial-setup/setup-your-email