What if they made a mistake on the airplane ticket and put the first name as the first name and last name?

A friend of mine booked a flight through Orbitz and they mistakenly put her first name as her first and last name, she is supposed to fly out in 3 days and just noticed the mistake yesterday. She called Orbitz and they will change the name but Continental Airlines will not make the change, they did note her file but said she will most likely not be allowed to fly. What can she do?