First, are you sure the names have been switched? Try to go to "Manage my booking" at Finnair to see what really is in their register. You access the booking by booking ref and the last name, and if that works, you are all OK.

If you can't access the booking with real last name, try the same with any first name in the booking. If that succeeds, then it seems names have been switched. If so, are the names correct in the confirmation from the travel agency? Then present this evidence to the travel agent.

If in fact you made the mistake at booking, then the advice given as to try to use the tickets anyway is what you should do. You should contact authorities along your route and ask what their policy is when names are sorted in wrong order. I believe (but have not experience of) that they are able to allow you to fly. The wrong sorting of names are not unheard of, because "first name" and "last name" does not really mean the same thing to people around the world.