Thank you so much for all your answer.
@LAXative: No, I book it through an agency based in Sweden.
@Guy Betsy: Yes, I acknowledge that my friend's situation is very complicated. As we put the LAST NAME completely wrong. It is due to the automatic filling feature of the web browser.
Do you think that they are reluctant to help us as the name is so difficult to change and the situation involves two airlines. But is there any chances that it is getting easier as the route inside Europe (Finland - Italy) operated by both airlines Cathay + Finnair. Can we just request name change to Cathay as a new ticket is issued any way?
Thanks again for all your reply.