This is a startling change for an organization that still has Ms. Sandberg’s face pop up when you scroll over the About Us tab on its website; as recently as October, she was the lead author of a Lean In-branded essay in The Wall Street Journal. It coincides with a radical shift in perception of Ms. Sandberg in her day job, as Facebook’s chief operating officer.

In recent weeks, Ms. Sandberg’s work at Facebook has been the subject of damaging headlines, from her slow response to Russian manipulation of Facebook to the way her team went on the attack against critics. Pundits have called on her to resign. Now, the Lean In movement is trying to figure out how independent it can actually become from the Sheryl Sandberg brand.

Ms. Sandberg’s workplace feminism revival began with her 2013 book, “Lean In: Women, Work, and the Will to Lead.” Research she popularized at the time — about how women do not negotiate as strongly as men do for raises, about how posing like Superwoman in the bathroom can help women stand more authoritatively for a presentation — is now mainstream. Her phrases became part of the lexicon.

But it was always going to be tricky to have a feminist movement led by a billionaire corporate executive. Now jabs at Ms. Sandberg make some crowds cheer. “It’s not always enough to lean in,” Michelle Obama said onstage in Brooklyn this month, while promoting her memoir. Using an expletive, Mrs. Obama added that Lean In stuff “doesn’t work all the time.”

For Ms. Sandberg, 49, none of this was the plan. She was widely expected to leave Facebook after the 2016 election and work for President Hillary Clinton, perhaps as secretary of the Treasury. When Mrs. Clinton lost, Ms. Sandberg continued at the company just as it became engulfed in crises.