I went on a ten-leg trip (boarding flights in the U.S., Singapore, India and Japan on either four or five different airlines) three years ago on tickets where the India-based travel agent had entered my family name as my given name and my given name plus my middle initial as my family name. Other than needing to tell a few check-in agents where to look up my reservation by name, I had zero problems in any way with anyone, including U.S. TSA agents.