You don't have the ability to edit a prepaid appointment to be for a different person, so you will need to cancel the appointment and reschedule it for the correct client.
If you cancel a prepaid appointment, the money is automatically converted to Store Credit to use at a later date. You can then subtract the store credit from the original client and add it to the actual recipient's record. You'd then book a new appointment for the recipient, and you can use the added store credit to cover the cost. The actual credit card charge will still be under the original client's record, but the store credit will take care of the new appointment.