Often yes, but not always, because the airline decides and not us. A small spelling slip in a first name or surname is accepted by many airlines as a correction, especially when the name on the passport is clearly the same person. Changing the ticket to a completely different traveller is a different matter and is usually not allowed at all, since the ticket belongs to the person it was issued for.
In practice you raise the correction as a request against the booking rather than editing the name yourself, and it is passed on to the airline. A few airlines handle this quickly, many need the request to be worked manually, and some will ask for a copy of the passport before they agree. There can be an airline charge for the correction, and low cost carriers tend to have their own rules that are stricter or more expensive than full service airlines. Because of that, we cannot promise in advance that any particular name will be corrected or what it will cost.
Timing makes a big difference. The sooner you spot the mistake and raise it, the better your chances, and it is much harder once online check in has opened or the flight has departed. If the airline refuses, the usual options are to cancel for whatever refund the fare allows and book again, which can mean losing part of the money.
The safest habit is to type the passenger name exactly as it appears on the passport at the time of booking, check it against the confirmation before you leave the booking, and raise a correction request straight away if anything looks wrong so we can ask the airline while there is still time.