When I was flying to the US on (late ie 2 months after wedding) honeymoon also on an award ticket - the Airline (British Airways) told me to book the ticket in the name on my passport. I had just renewed my passport earlier that year and ws too tight to pay the change fee they required.
I was told that it would make a big difference to getting ionto and out of the US.
I travelled everywhere in my maiden name until my daughter was born and I had to add her to my passport, so made the change at that time - about 3 years later.... but I booked tickets in maiden name until then - even when visibly pregnant !