Thanks for the answers! Most interesting, certainly the part that some rights don't apply at airports.
I am not planning to mess with CBP, but indeed if TSA is power tripping on me, by for example asking my name when I provided photo ID and BP, I will refuse to answer. In that case I wanted to double check they can't do anything with their threats like 'you have to answer that or...'.
As I understand they HAVE to let you through unless you have forbidden items or do not cooperate with screening. Refusing answering at the BP check is no ground for them?