Mr. Pierluisi, a lawyer, could have a conflict of interest because he works for a firm that does external legal consulting for the unelected federal oversight board that oversees Puerto Rico’s finances. On Tuesday, Mr. Pierluisi was placed on a leave of absence from the law firm, O’Neill & Borges.

His brother-in-law, José B. Carrión III, remains the chairman of the federal oversight board. The New York Times found in 2016 that Mr. Pierluisi introduced legislation as resident commissioner that would benefit at least two Wall Street companies that had hired his wife, María Elena Carrión, for financial advice. (Mr. Pierluisi and Ms. Carrión are in the process of divorcing, the Puerto Rican news media have reported.)

Mr. Pierluisi’s ties to the unpopular oversight board do not sit well with some lawmakers. Several went on television to call his nomination unacceptable.

“No one can question his abilities,” Representative José Meléndez, a member of the New Progressive party, told WAPA, a local station. “But I saw him in meetings with the board, and he was on the side of the board. That puts him in conflict with government policies. He’d probably have to recuse himself. It’s going to be very difficult for him to govern without access to the fiscal control board.”

Senator José Antonio Vargas Vidot, a political independent, chided the statehood party for not looking outside of its usual ranks for a nominee. “It’s as if the PNP doesn’t have anyone without a conflict,” he told WAPA.

Yet Gisela Gómez, 45, who sells homemade sweets to tourists in San Juan, the capital, said she participated in the massive march last week to oust the governor and was pleased with Mr. Pierluisi’s selection.

“We have to run all of the corrupt ones out, and replace it with a new government,” Ms. Gómez said. “I don’t know much about politics, but from what I have heard, of all of them out there, he is the best one.”