Priceline.com Adopted Child - We found her. Booked a/l ticket under wrong name will not change name, but will cancel for $150.00 and rebook. Norrwalk, Connecticut

I find it very hard that in talking to someone for the first time in 42 years that in the several months you were talking to her you never "caught up" and asked if that was her current legal name. 

She may very well be divorced, newly married, separated or for all you know her name was a nick-name where her ID had her legal name.  I know several people who do not use their full legal name on any Social Networking site because they are fearful of Identity Theft.

The tickets you got were discounted tickets.  Unfortunately when you buy them they are NON-REFUNDABLE and NON-CHANGEABLE, and these are terms you agree with when you bought the tickets.  And yes you did agree to them by most likely putting your initials in a box on the website that said you READ and AGREE to the terms.  It really won't matter who you got the tickets through as most have this same restriction on discounted fares. 

Anyways with all of that said.  If she is recently married she can get an OFFICIAL copy(from the county where the marriage was performed) of her marriage certificate and along with her current ID showing her maiden name TSA and the airline SHOULD allow her to fly.  If this is a case where she is going the other way(Married now divorced).  She may be able to reverse this process and show a certified copy of her divorce decree(as those generally include name change orders) along with her current ID.  Although you may still want to confirm these cases.