Add clinic name to form submission email

I have 2 clinics with 2 separate email addresses and staff and we have the same appointment types and therefore custom forms for both clinics. I would like if you can add the clinic name to the form submission email, then I can create an email filter that will send the submission email to the right clinic. At the moment I can only select for the forms to go to one clinic so that clinic receives unnecessary submissions and the other clinic is never notified.