You will have no problem flying. My current passport of two years has my first, middle and last names all in the wrong fields (which means the name on my tickets never matches that on my passport if you look field by field) and I have not had any problems flying with it to over a dozen countries (or getting visas where required, for that matter).

As Guy Betsy said, the only problem you will have is when trying to get miles as your name in your FFP will not match that on your ticket. Usually resolved by sending in a copy of your boarding passes with a misisng mileage claim.