Sometimes yes, but this depends far more on the airline than on the booking system. A small spelling fix, such as one or two letters in a surname, is allowed by many airlines and can often be handled without cancelling anything. Putting a completely different person on the ticket is almost never allowed, and in that case the usual route is to cancel if the fare rules permit it and book again.
What you actually see on your portal depends on what the flight API supports. Some suppliers accept a name correction request straight from the booking screen and pass it to the airline for you. Others only let you raise the request, and it then has to be followed up with the airline before the ticket is updated. Low cost carriers often behave differently from full service airlines, and some treat any name change as a paid change rather than a correction, so the system can carry the request but it cannot promise the outcome.
Because of that, the safest habit is to catch the mistake before the ticket is issued. Most portals give you a final review step showing the passenger details, and it helps to ask your customers to type names exactly as printed in the passport rather than the short name they use every day. Checking the ticket as soon as it arrives also works in your favour, since airlines are often more flexible shortly after issue than close to departure.
If you have a wrong name on a live ticket right now, open the booking in your system and look for a name correction or amendment option, and if there is none, send the request to our support team with the passport page so it can be taken up with the airline.