Every confirmation email links to the customer's own booking page, which has Need to change or cancel? on it. Change the time offers the next two weeks with the same service and person, in one press, and you are told when they do. Cancel puts the time back on sale. There is no login: the link is theirs.
You decide how late they can do it. Under Shop settings, Booking rules, Cancelling and payment, Cancel up to is Any time, or 2, 12, 24 or 48 hours before. Inside that window the page does not let them cancel or change the time; it tells them to ring you, with your number. A customer who wants someone else cancels and books again.
When a customer cancels in time a booking that carries money, If they cancel in time is your rule: Ask me first (the default, and the email tells you it is your call), Refund it all, automatically, or Keep the deposit, refund the rest. Card money goes back to their card through your own Stripe. A no-show refunds nothing by itself.
You can cancel or move any booking yourself, at any time, from the diary. A cancellation emails the customer an apology and puts the time back on sale, and offers it to the first suitable person on that day's waiting list. A move emails the new time unless you untick that box.