Secretary of State George P. Shultz moved quickly to put his imprint on the State Department hierarchy yesterday as President Reagan announced he would nominate Kenneth W. Dam, a close friend of Shultz, to be deputy secretary of state.

Dam, 49, a law professor and provost of the University of Chicago, wrote a book with Shultz in 1977 and was described by Shultz yesterday as a "friend of many years."

He will succeed Walter J. Stoessel Jr., the highest-ranking Foreign Service officer, who ran the department after the abrupt resignation last month of Alexander M. Haig Jr. Stoessel is retiring but is expected to remain as a consultant.

Reagan also announced two other top State Department appointments yesterday, at least one of which was in preparation while Haig was still secretary.

W. Allen Wallis, chancellor of the University of Rochester and a conservative economist, was tapped to be undersecretary of state for economic affairs. Wallis, 69, will fill a post that had been open for several months following the resignation of Myer Rashish in a policy dispute with Haig.

Shultz told a meeting of his senior staff yesterday that Wallis was his choice for the job, according to one department official. A friend of Wallis added, however, that Wallis had been approached by Haig several months ago about the position.

William Schneider Jr., 40, currently associate director of the Office of Management and Budget for national security and international affairs, will be nominated as undersecretary of state for coordinating security assistance programs. He fills the vacancy left by James L. Buckley, the former Republican-Conservative senator from New York, who moves to become counselor to the department. His move had been previously announced by Haig.

All the nominations require confirmation by the Senate.

Also yesterday, Dean Fischer, the former Time magazine correspondent who was chief spokesman for Haig, said he had informed Shultz on Saturday of his desire to "return to private life." Fischer said he has "no specific plans" and agreed to remain until a successor is found.

In a few minutes of light banter in the State Department diplomatic lobby, Shultz was officially welcomed by several hundred applauding career department employees and promised to make use of them in carrying out Reagan's foreign policy.

"I fully intend to call on you. . . . I know I need you, and I know you will pitch in," he said. "I guess my final word is that I expect to work the hell out of you and I hope you'll come through. I know you will."

Shultz was sworn in Friday as the nation's 60th secretary of state and conferred at length Saturday on the Mideast crisis with former secretary Henry A. Kissinger.

Dam, who has known Shultz since the 1960s, was an assistant director of OMB for national security and international affairs when Shultz was director of the budget office in the Nixon administration. Their book was entitled "Economic Policy Beyond the Headlines."

Wallis has been affiliated with the University of Rochester since 1962. While retaining his title of chancellor, he turned over chief executive responsibilities at the school in 1975. He served on the Reagan transition team for the International Communication Agency.

Schneider, an economist and defense analyst, had served previously on the House defense appropriations subcommittee and as a consultant to the Hudson Institute.