I recently booked an international flight via United (outbound on Austrian Airlines and inbound on Luthtansa) using an agent on the phone.

When I checked the booking online, I noticed that they had spelled my wife's middle name incorrecctly ( ."..eddy" insttead of "...eedy")

When I next talked to the United agent, she said she would have had to cancel the reservation in order to fix the error. She said that if she did that I would lose that slot (frequent flyer purchase) so should could not fix the error.

She did say she would note the error on our file.

Do I have a problem and what should I do about it?