If my customer's payment goes through but the booking does not complete, will I know about it?

Yes, you will be told when that happens, and it helps to understand why it happens at all. A booking is really two separate steps, taking the money and confirming the seat or the room with the supplier. Almost always they run one after the other in the same moment, but if the supplier does not answer in time, or the fare is taken by somebody else while your customer is paying, the payment can succeed while the confirmation does not.

When that happens the booking is not quietly dropped. It stays in your system with a status that marks it as unfinished, and it shows in your bookings list so your staff can see it for themselves instead of finding out when the customer calls. Most agencies also set up an alert so whoever is on duty is told straight away, because the sooner someone looks at it, the better the chance the same fare is still there.

What you can do next depends on the supplier. Sometimes your staff can simply retry the confirmation and it goes through on the second attempt. Other times the fare has gone, and the choice is to move your customer onto the next best option or to refund. Refunds follow the rules of your payment provider and of the supplier, so the money can take several working days to reach your customer even when you release it the same day.

Ask whoever set up your portal to show you exactly where unfinished bookings appear and who receives the alert, and agree with your team what they should say to a customer while it is being sorted out.