Lists of names of those the president-elect is said to be considering are flying across Washington, prompting lawmakers and interest groups to raise questions about some top contenders.

WASHINGTON — There are leading candidates and dark horses. There are potential roadblocks from progressives and conservatives. And there are competing factions hoping to be part of the next president’s inner circle, all jockeying for influence.

President-elect Joseph R. Biden Jr. moved quickly this past week to name the first two members of his cabinet, picking one of his closest confidants to be the nation’s top diplomat and choosing an immigrant to lead the Department of Homeland Security, a first.

But as Mr. Biden fills out the rest of his team in the days and weeks ahead, the task will become more complicated, requiring him to navigate tricky currents of ideology, gender, racial identity, party affiliation, friendship, competence, personal background and past employment.

Aides to Mr. Biden who are managing the selection process are revealing little about whom he intends to choose. And yet, as is typical in Washington in the early days of a transition, the names of those the president-elect is said to be considering are a frequent source of discussion. This time, the gossip is spreading via Zoom calls, Twitter posts and encrypted text messages sent by lawmakers, lobbyists and political consultants.

“I can assure you, there will be more cabinet announcements in the weeks ahead, so buckle up for December,” Jennifer Psaki, a senior transition adviser, told reporters this past week.

Whom Mr. Biden will tap to be the next attorney general is among the most talked about — and politically fraught — decisions that he will make as civil rights issues roil the country and some Democrats expect investigations into President Trump and his associates.

Sally Q. Yates, the deputy attorney general in the final years of the Obama administration, had long been considered the front-runner. Mr. Biden is close to her and has told friends that he could imagine her as the nation’s top law enforcement official. But some advisers fear that Republicans would block her nomination because of her refusal to defend Mr. Trump’s first travel ban and her role in the early stages of the investigations into his campaign and his associates.

Mr. Biden could instead pick Lisa Monaco, the former homeland security adviser for President Barack Obama who was a finalist in 2013 to be F.B.I. director. And like Ms. Yates, she worked well with Mr. Biden when he was vice president.

But both women are up against Deval Patrick, the former Massachusetts governor who served as the head of the department’s civil rights division in the Clinton administration and would be the second Black man to be attorney general.