Do I need to re-create a reminder if an appointment is rescheduled?
No, even if a reminder has already been sent for the original appointment a new reminder will be created with the new appointment details.
If you're a business that moves appointments around lots leading up to the actual appointment date we do have an option to NOT trigger any new reminders for appointment changes made in the 24 hours before the appointment start time.
Please note: This article relates to Google Calendar. If you are using a different calendar this article might not be applicable.