WASHINGTON — President Trump on Monday named Randal K. Quarles, a former Treasury Department official, to serve as the Federal Reserve’s top watchdog overseeing Wall Street and to play a leading role in the administration’s plans to reduce financial regulation.

Mr. Quarles would be the first person to serve in the role of vice chairman for supervision, which Congress created after the financial crisis to sharpen the Fed’s focus on regulatory issues. As a member of the Fed’s board of governors, he would also have a vote on monetary policy.

The position requires Senate confirmation, but Republicans, who hold a majority, can confirm Mr. Quarles without support from Democrats, should that be necessary.

Mr. Quarles, 59, would be a counterweight to the Fed chairwoman, Janet L. Yellen, who has led the Fed’s postcrisis stimulus campaign and its efforts to strengthen financial regulation.