Summary
The process of refunding a payment made to the wrong customer depends on the payment method.
Key Points
If the payment was made with PayPal or Stripe, make the refund there
If it's a direct deposit or an electronic funds transfer contact the 'wrong' customer's bank to initiate the refund
Apply the payment to the right customer
Delete the original payment
If it's a credit/debit card, apply the credit card refund to the 'wrong' customer. If using PayPal or Stripe, log in to the payment service (paypal.com or stripe.com). Click the 'refund' button on the payment you would like to refund.
If it's direct deposit or EFT (electronic funds transfer) contact the 'wrong' customer's bank to initiate the refund.
For any of the methods above, after the refund process has begun, apply the payment to the right customer.
If it's cash or check, go into the 'wrong' customer's account and delete the payment. Go into the correct customer's account and add the payment
FYI, for security purposes, Stripe and PayPal do not allow moving cards or charges between people. The payment will need to be re-entered. This means you might have to contact the customer to re-obtain the credit card information and make the payment to their account.