I'm not familiar with Award Magic, but did they book direct on iberia.com? The reason I ask is because that might influence IB's willingness to help you. My story was like this...

My IB+ account had my last name twice. I suspect that happened when I created my account I had to put first last name + second last name on my file, according to Spanish naming conventions. I'm not Spanish, and I only have one first name and one last name. In three years, I had never had a problem to accrue points (all my work travel was booked through corporate agent). The first time I bought tickets directly at iberia.com, I just used the data on my IB+ file to automatically fill out all fields, didn't notice the two repeated last names while booking, and the ticket was had my full name wrong. Both last names were in the "last name" field of the reservation, which to me seems worse than if the "first last name" being at the "first name" field of the reservation. I ended up emailing IB+ about it, explaining what happened (I'm IB+ Gold) and they fixed it for me in a few weeks, both in the ticket and in my IB+ account. I suspect they did that because it was wrong in the first place at my IB+ file and also because I booked directly at iberia.com.