With the introduction of Calendar HQ, not only can your clients reschedule appointments, your users will also have the ability to reschedule too:

The scheduled user on the appointment will receive a confirmation email when the appointment gets scheduled by the user and also when the appointment gets rescheduled.
We're introducing a new variable in the email templates that allows you to distinguish who rescheduled the appointment; whether it's your client or someone on your team. The new variable, called "Person Who Rescheduled (Client or Technician)" can be used in any editable email template where you'd want to indicate who rescheduled the appointment such as a "rescheduling confirmation" template:
