WASHINGTON — There is usually no quicker way to make Rand Paul’s face pucker than to ask him how he is different from his father. That is because for the better part of four years, the Kentucky Republican has tried to create a political identity distinct from the man whose legacy provided the foundation for his success.

That inherent tension was never far from the surface. He tapped into the robust network of Ron Paul activists and supporters to build campaigns for Senate and the White House, often insisting, “I want to be judged by who I am.” Sometimes, when he was feeling less generous, he declared the entire father-son line of questioning off limits.

But as he wages his lonely fight against the National Security Agency’s surveillance dragnet, temporarily forcing a lapse in the law that gives the government wide discretion in collecting Americans’ phone-call data, Mr. Paul is publicly embracing the libertarian-hued philosophy that is synonymous with his family name.

“Often we use fear, and we say, ‘We won’t be able to catch terrorists,’” Mr. Paul told the conservative radio host and author Laura Ingraham on Monday, describing in Orwellian terms the threat he said the N.S.A. posed to civil liberties.