I don't think you'll have any problem. My UK passport has my full name on it, but in France people really don't use middle names much, so that all my French-issued cards (not only Flying Blue, but Bank Accounts, Social Security, Credit Cards and other Loyalty Reward cards) show only my first name and surname. So the name on my ticket and the name on my passport are never exactly the same. Indeed, if I book using my Flying Blue profile, my full name would be refused as invalid. No-one has ever questioned the anomaly at check-in or immigration in the US or anywhere else in the world.