A moderate who has criticized left-leaning Democrats, Mr. Adams has named several Republicans to his administration, including James Oddo, a former Staten Island borough president who is chief of staff to the deputy mayor of operations, and Eric Ulrich, a former City Council member from Queens who was named senior adviser. He also named Edward Mermelstein, an international real estate lawyer from Ukraine who has said he was friendly with former President Donald J. Trump, as commissioner of the mayor’s office of international affairs.Mr. Adams, who is the city’s second Black mayor, has received praise for the diversity of his cabinet. He named five women as deputy mayors; his police commissioner, schools chancellor and other top appointees are Black; and his transportation commissioner, Ydanis Rodriguez, is from the Dominican Republic and has been a leader on issues important to immigrant communities.Still, questions continue to follow his appointments. It is unclear if Philip Banks could obtain a top secret F.B.I. security clearance. The new correction commissioner, Louis A. Molina, fired a top investigator who examined complaints against officers for use of force.More news reports followed: Mr. Pearson ruffled feathers by proposing the removal of police officers from City Hall, WNBC-TV reported. Carlo Scissura, who could lead the city’s Economic Development Corporation, helped secure real estate deals without being registered as a lobbyist, The City reported.Many of those joining Mr. Adams’s administration stood by his side during a bitter and competitive Democratic primary last year, which he won by fewer than 8,000 votes. Brendan McGuire, a well-respected former federal prosecutor in Manhattan who will be his chief counsel, served as an adviser to Mr. Adams during his campaign and his transition.“I don’t do a lot of new friends,” Mr. Adams has been known to say.Joseph J. Lhota, a former deputy mayor under Mr. Giuliani who is now a Democrat, called criticism of Mr. Adams’s appointments “shallow and self righteous.”“The mayor has every right to select his team,” Mr. Lhota said. “Evaluation and criticism should be held for performance.”