In addition to the information from the other answers, to overfly the US, the airline will have to pass your information to the US CBP according to Secure Flight.
Since November 2010, Secure Flight has conducted watchlist matching of
passenger information against the TSDB for all covered U.S. and
foreign flights into, out of, and within the United States, including
point-to-point international flights operated by U.S. airlines. Secure
Flight also performs watch list matching for flights that overfly, but
do not land in, the continental United States.
As long as you are not (or someone named the same as you is not) on any of the TSA no-fly or other watch lists, this shouldn't affect you.