If the error is only one letter is should not be a problem. Some airline call centre staff don't really know the rules and will automatically say no and try to force you into buying another more expensive ticket. If the error is more than this I'm afraid you will either have to pay a hefty change fee (if the airline allows this) or buy another ticket.
Airlines may be difficult because they are worried they will be fined by immigration authorities. I suggest you talk to immigration at your final destination and get them to say what their position is. Get the name/phone number of the person you speak to so that you can inform the airline if necessary.
Finally, do not mention this problem to airline staff unless they ask. Most don't want to take responsibility and their default setting is NO.