I purchased an airline ticket to fly from New Orleans to Rome from Alitalia. It turned out to be a code share flight on Delta. At the check-in counter with Delta, it was discovered that I had entered my name incorrectly on the ticket; I had reversed my first and last names. Delta could not correct the error because it was an Alitalia ticket, so I had to call Alitalia for help. Alitalia said I was at the airport and they could do nothing about the error. The Delta agent tried to tell Alitalia the reservation was open and a change could be made, but Alitalia refused to help. My family and I had booked a ten-day tour through Italy set to begin the next day. What to do? Delta said that I would have to purchase another ticket, and they would try to secure one for the price I had paid Alitalia. Then I could request a refund from Alitalia. By this time, over an hour had passed. These agents had no idea how to process a new ticket; I requested a supervisor but no one came. Another half hour passed and the agent was still on the phone for assistance with the ticket. My family is now at the gate; the plane is beginning to board - I am at my wit's end when one of the agents comes up with a ticket - three times the price of the original ticket. Yes, she charged me for a walk-up, same day ticket. Not knowing what else to do, I handed over my credit card. I am home now trying to deal with this. I asked Delta for an adjustment on the $2800 I was charged. They refused and offered to request a refund from Alitalia for the unused ticket. Had it been a Delta ticket, the error would have been corrected at the counter. The code share throws a wrench into the mix that no one seems to be able to deal with. It boggles the mind that I paid almost $4000 for an economy ride to Europe. Any ideas on how to deal with this? I have called and written to various departments at Delta, and I have spoken to my credit card company. I need some direction from more seasoned travelers as to how to deal with this airline.