Mike Donilon is one of Biden’s most trusted White House presidential advisers, but he comes and goes from his West Wing office almost like a spectral presence.

Described by those who worked with him as having the demeanor of a parish priest, he hates talking to the media and is not particularly talkative with his own colleagues. On conference calls, they describe him as a talker. “Hey, it’s Mike,” he will say, often in a barely audible voice.

Mr. Donilon’s low-profile presence is emblematic of Biden’s overall White House culture: it is the least personality-oriented West Wing in decades.

Because of his longevity in politics and his personality as an outsider, combined with the depth of the crises he faces, President Biden is undoing a long Washington tradition in which staff members enjoy their own refracted fame.

The phenomenon was pronounced during Donald J. Trump’s presidency – his advisor Kellyanne Conway was so well known she needed her own security details; White House press secretary Sean Spicer was a recurring character on “Saturday Night Live”; Hope Hicks, director of communications, was regularly photographed by the paparazzi as she left her home in sportswear. But Mr. Trump did not invent the celebrity staff.

“Each White House takes on the personality of the president,” said Paul Begala, former adviser to President Bill Clinton, who himself became a well-known figure after appearing in “The War Room,” a documentary on the Clinton campaign by 1992.

“President Clinton did not hesitate to have famous employees,” said Mr. Begala. “He appreciated. There is a blue collar sensibility with Biden and his team. You carry your bucket to work, you point the clock. You show up every day and do your job.