Amy Gleason, a former health care investment executive, is serving as the acting administrator of the Department of Government Efficiency, the government-overhaul task force imposing dramatic changes across the federal bureaucracy under the direction of Elon Musk, a White House official said on Tuesday.

For two weeks, the Trump administration had resisted answering inquiries about who was formally leading the effort, which reports to the White House. Mr. Musk, who is the world’s richest man and a key adviser to President Trump, has been clearly driving the initiative, including by instigating an email to all federal employees on Saturday that instructed them to list their accomplishments during the last week.

But the White House has insisted in court that Mr. Musk is not the administrator of the cost-cutting team, adding to the sense of opacity surrounding it. On Monday, a federal judge pressed the government for clarity about the billionaire’s role, expressing concern that unauthorized individuals were effectively running the office.

On Tuesday, a name was revealed: Ms. Gleason is the temporary leader of what is formally known as the U.S. DOGE Service, according to the White House official, who was not authorized to speak publicly.

Mr. Trump created the office on Inauguration Day through an executive order, transforming a White House tech unit that had been established under President Barack Obama. Since then, staffers hired by Mr. Musk and his aides have fanned across the government and sought access to sensitive databases, scrutinized federal employees and even tried to shutter whole agencies.

Ms. Gleason did not immediately respond to a request for comment. She was scheduled to be on vacation in Mexico on Tuesday and told associates that she was not aware ahead of time that the White House planned to make public her role, according to people familiar with the situation, who spoke on the condition of anonymity out of fear of retaliation.