Sometimes yes, but the answer comes from the airline rather than from us. Small spelling corrections, such as a letter or two in a first name or surname, a missing middle name, or a first name and surname entered the wrong way round, are allowed by many airlines and can be requested through the flight booking API after the ticket is issued. Changing the ticket to a completely different traveller is almost never permitted, because an airline ticket belongs to the person named on it.
What counts as a minor correction is not the same everywhere. Some airlines will fix a genuine typo free of charge if you raise it soon after issue. Others treat any change to the name as a cancellation and a fresh booking, which means the original fare rules apply and your customer may not get back everything they paid. Budget carriers usually allow a correction but charge a name change fee, and it can apply per passenger and per flight. We cannot promise a particular result because the rule belongs to the carrier and not to us.
On our side, the request goes through the system and we pass it to the airline or the supplier, and you are told whether it has been accepted, whether a fee is due, or whether the airline wants to handle it directly. Not every correction can be done automatically, so in some cases our support team has to file it with the airline by hand, and that takes longer than an instant confirmation.
The safest habit is to check every name against the passport before you issue the ticket, and if you do spot an error, send us the booking reference the same day so we can approach the airline while the easiest window is still open.