While some White House officials had insisted that Mr. Trump was pleased with Mr. Giuliani’s performance on Fox News in an interview with Sean Hannity on Wednesday night, two people close to the president painted a different picture. They said that Mr. Trump was displeased with how Mr. Giuliani, a former New York mayor, conducted himself, and that he was also unhappy with Mr. Hannity, a commentator whose advice the president often seeks, in terms of the language he used to describe the payments to Ms. Clifford.