Associate Deputy Attorney General Stanley E. Morris, a close adviser to Attorney General William French Smith, was sworn in this week by Chief Justice Warren E. Burger as the new head of the U.S. Marshals Service.

The appointment of Morris, 41, a non-lawyer and career government employe, is expected to bring the marshals under closer supervision of the Justice Department. Until recently, the marshals largely operated on their own although they were technically under the department's jurisdiction.

The marshals service has come under some congressional criticism because of its handling of the controversial witness protection program, under which cooperating witnesses--most of them criminals--are resettled around the country under new identities.

The marshals service, made up of 93 U.S. marshals appointed by the president and 2,000 deputy marshals, also has many other responsibilities, ranging from security in federal courtrooms to the serving of federal subpoenas.

Morris is known at the department as a skillful, behind-the-scenes operator who played a central role in heading off budget cuts planned by the Reagan administration for the Justice Department while other domestic agencies were taking large cuts.

He succeeds William E. Hall, who has been named assistant associate attorney general for law enforcement training. REYNOLDS RESOLUTION . . . . Rep. Richard L. Ottinger (D-N.Y.) has submitted a resolution in the House calling on President Reagan to fire William Bradford Reynolds, head of the Civil Rights Division.

The resolution, which is being circulated among other members of the House, was sparked by reports that Reynolds had attempted to block the NAACP Legal Defense Fund from intervening in a South Carolina school desegregation case, urging division lawyers to make "those bastards . . . jump through every legal hoop" before becoming parties to the case.

Reynolds has said through a spokesman that he does not recall using those specific words, but that he did use words to that effect because he considered the defense fund, which was representing parents of black school children, to be legal "adversaries" in the case. NAMES AND FACES . . . Peter Vaira, the veteran prosecutor who recently resigned as executive director of President Reagan's Commission on Organized Crime, has joined the Chicago law firm of Lord, Bissell and Brook. Vaira reportedly left the crime commission because of disputes with U.S. Appeals Court Judge Irving Kaufman of New York, who heads the commission.