Another Goldman Sachs executive is being hired for a senior government role in Washington — this time at the Treasury Department.

James Donovan, a longtime Goldman banking and investment management executive, has been named to be the deputy to the Treasury secretary, Steven Mnuchin.

Mr. Donovan, 50, would be responsible for helping Mr. Mnuchin, also a Goldman alumnus, in running a government agency that handles a wide range of economic matters, from producing physical currency to enforcing economic sanctions against nations.

President Trump also said on Tuesday evening that he would nominate David Malpass, a former Treasury official under Presidents Ronald Reagan and George Bush, to be undersecretary of the Treasury for International Affairs. Four others were named for senior positions in the Treasury Department.

Mr. Donovan’s addition makes him the fourth Goldman veteran to be named to a senior role in the Trump administration. Gary D. Cohn, director of the National Economic Council in the White House, is a former No. 2 at the firm while Stephen K. Bannon, Mr. Trump’s chief strategist, was once a banker there.

The number of former Goldman Sachs executives now operating at the pinnacle of government has raised questions about whether the firm will have undue influence over policy that may benefit it, especially as Mr. Trump pushes for a wave of deregulation intended to benefit an array of American companies, including banks.

Indeed, the White House appeared to have hesitated over the naming of Mr. Donovan, given those questions.

Democratic lawmakers, including Senators Elizabeth Warren of Massachusetts and Tammy Baldwin of Wisconsin, have been critical of the Goldman Sachs hires, and on Feb. 9 they issued a letter demanding information about whether Mr. Cohn and others had communicated with the firm’s current leadership about public business.

In a recent response, Goldman’s general counsel wrote that the company was aware of the “applicable rules and guidelines for interactions with government officials” and had “no reason to believe that individuals from Goldman Sachs breached them.”

As deputy Treasury secretary, Mr. Donovan will play a substantial role in shaping some of the Trump administration’s biggest priorities.

Overhauling the nation’s tax code, which the White House has argued will make American businesses more competitive with their overseas counterparts, is at the top of that list. In recent interviews, Mr. Mnuchin set a goal of having legislative approval for a new tax package before Congress takes its August break — even as objections to Republican plans for a repeal of the Affordable Care Act threaten to delay that legislation and, with it, the tax modifications.

Mr. Donovan has spent nearly 25 years at Goldman, where he worked with companies and individuals both as an investment banking adviser and as an investment management overseer.

Through the years, one of his biggest clients has been Bain Capital, a private equity firm whose business involves acquiring and overhauling companies. As an outgrowth of that, Mitt Romney, a Bain founder, became an individual client managed primarily by Mr. Donovan. (A representative for Mr. Romney did not respond to a request for comment.)

A longtime Republican, Mr. Donovan subsequently acted as an economic policy adviser to Mr. Romney during his 2012 presidential campaign and donated thousands of dollars to Mr. Romney’s run, according to federal filings. More recently, Mr. Donovan donated $95,000 to a political action committee that supported Jeb Bush in the Republican primaries last year.

In addition to his job at Goldman, Mr. Donovan, who lives with his wife and four children in Virginia, teaches corporate strategy and business ethics at the University of Virginia’s law school.

Jason Jones, an associate in a corporate law firm in Salt Lake City who took Mr. Donovan’s courses in law school, said he gave memorable advice on topics like mentoring and time management.

In large seminars and in small group meetings with students, Mr. Jones said, the topics ranged from “how do you maintain your sanity as a very successful investment banker” to “how do you view current topics?”

“He was willing to talk about anything,” Mr. Jones said.

Mr. Donovan joined the Trump transition team after meeting Jared Kushner, Mr. Trump’s son-in-law, through a friend last year and has spent recent months helping Mr. Mnuchin with Treasury staffing, associates say.

Mr. Mnuchin and Mr. Donovan will tackle not only changes to the corporate and individual tax codes but also the potential restructuring of the government-sponsored mortgage guarantors Fannie Mae and Freddie Mac.