Add the name and phone number of the patient in the title / summary of the appointment. Check out how to use the summary of the appointment to add the patient's data:
Now, if you need to have a contact card, and since Holly doesn't use the email to contact your patients, you can add fake email for any person for whom you don't have a real email address.
You can use the domain @myholly.net to identify the fake emails; i.e. email@example.com. Just remember that you can't have two persons with the same email, even if it's a fake one!