On the same day that the Trump Organization announced its appointment of two ethics monitors to advise on potential conflicts of interest, it faced a new ethical quandary: Is it right to double the price of the initiation fee at Mar-a-Lago, the Trump family’s private club in Florida, or would that be seen as cashing in on President Trump’s arrival in the White House?

The question emerged after Bernd Lembcke, the managing director of the 118-room club in Palm Beach, Fla. — which Mr. Trump recently labeled the Winter White House — confirmed on Wednesday that the price of new memberships had increased to $200,000 from $100,000, and that applications had surged since Mr. Trump won the election in November.

Mr. Lembcke’s acknowledgment came hours after the Trump Organization announced that it had named Bobby Burchfield, a longtime Republican Party lawyer and corporate litigator, as an “independent ethics adviser.” The Trump Organization pointed to the move as a sign of its commitment to addressing questions about potential conflicts of interest.

“We take our role and the responsibility we have to our company, and our thousands of employees, very seriously,” Eric Trump, one of the president’s sons and an executive vice president of the Trump Organization, said in a statement announcing the appointment of Mr. Burchfield.