NEW YORK — President-elect Donald Trump hadn’t been seen in public for days when he walked into New York’s 21 Club to applause from fellow diners. The unannounced evening out with family was a contrast to the behind-the scenes machinations that suggested a struggling transition as names surfaced and sank for top administration positions.

Not to worry, Trump suggested in a Tuesday night tweet: “Very organized process taking place as I decide on Cabinet and many other positions. I am the only one who knows who the finalists are!”

Before dinner at the midtown Manhattan restaurant— he broke with protocol and left his press contingent behind — Trump met with the head of his transition team, Vice President-elect Mike Pence, but another day passed without a Cabinet announcement.

Strains were showing within the process. Trump’s allies engaged in an unusual round of public speculation about his potential appointments. Former Rep. Mike Rogers, a respected Republican voice on national security issues, quit the transition effort. And an apparent clerical oversight effectively halted the Trump team’s ability to coordinate with President Barack Obama’s White House.

Former New York Mayor Rudy Giuliani seemed to be angling for secretary of state. But Trump’s transition team was reviewing Giuliani’s paid consulting work for foreign governments, which could delay a nomination or bump Giuliani to a different position, according to a person briefed on the matter but not authorized to speak publicly about it.