If my customer's name is spelled wrong on a flight they have already booked, can I correct it myself on the portal?

In most cases no, a name correction is not something you can push through on your own from the portal. Once a ticket is issued, the passenger name sits in the airline's own record, and airlines treat names as a security matter, so the carrier decides whether a correction is allowed, what evidence it wants and what it charges. What the portal can do is show you the booking exactly as it was sent, including the name fields, so you can see where the mistake happened and raise the request with your supplier straight away.

How much is actually possible depends on the airline and on what the flight API passes through. Some carriers accept a small spelling fix, a swap of the first and family name, or a missing middle name being added, and a few of those requests can be sent through the API so they reach the airline without a manual message. Other carriers will not amend a name at all and expect the ticket to be cancelled and rebooked, which means the original fare rules apply and the fare you resell may not be the one you originally quoted. Low cost carriers usually run their own separate process again.

Timing matters more than anything else. If the error is spotted very soon after ticketing, some tickets can still be voided and reissued cleanly, but once that window has passed it becomes a change or a cancellation with whatever rules the fare carries. We cannot promise a particular outcome for a particular airline, because that sits with the carrier and with your supplier agreement.

The safest step is prevention, so check passenger names against the passport before you issue, and ask your supplier for a list of which airlines they can correct names with and how long you have to do it.