Secretary of Defense Richard B. Cheney yesterday named Henry F. Cooper, a former U.S. arms negotiator and strong advocate of space weaponry, to become third director of the Strategic Defense Initiative (SDI) program that is aimed at developing a comprehensive defense against Soviet ballistic missiles.

Cooper, whose selection is not subject to Senate confirmation, inherits a program that faces what some officials are predicting will be the most intense funding fight in its six-year history. Some legislators are proposing that its $3.8 billion fiscal 1991 budget be cut by 40 percent, while the Pentagon insists on a 22 percent increase.

The program is facing an identity crisis due to warming U.S.-Soviet relations, which many experts say have dimmed the likelihood of a strategic conflict, and which have prompted some U.S. allies to advocate direct economic aid to Moscow.

While some experts have advocated that SDI be reduced and redirected toward the threat of an accidental strategic missile launch or regional attack by tactical missiles, Cooper recently completed a special SDI review for Cheney by urging that it remain focused on protecting the United States from an all-out Soviet assault.

He said in a telephone interview yesterday that his primary goal will be "to try to help the secretary focus the program and move toward picking the exact architecture for a feasible defense. . . and hopefully move toward deploying defenses as soon as the program can demonstrate they are feasible."

He said he shares Cheney's "commitment to making it happen."

Cooper, SDI's first civilian manager, indicated he will replace senior officials who have recently retired, including the program's chief scientist, deputy director and chief of staff.

As an Air Force deputy assistant director for research in the early 1980s, Cooper played a key role in developing a small rocket that was to be launched from F-15 fighters at orbiting Soviet satellites. The program was canceled several years ago due to technical problems and congressional opposition to space weapons tests.

As chief U.S. negotiator on defense and space matters from 1987 to 1989, Cooper strongly supported the Reagan administration's controversial "broad," or permissive, reading of the 1972 Anti-Ballistic Missile (ABM) Treaty, allowing virtually unlimited tests of sophisticated space weaponry. Congress has repeatedly barred such tests as a violation of the "narrow," or traditional, reading of ABM constraints.

Cooper said yesterday that he believes the program's current plan to orbit thousands of small interceptor rockets, known as "Brilliant Pebbles," has "a lot of promise." His predecessor, Air Force Lt. Gen. George Monahan, estimated recently that deploying such a system would cost $45 billion, but others have said the lifetime costs would be nearly $100 billion.

The Brilliant Pebbles system would be aimed at defending against less than half of Soviet missiles launched in an all-out attack, allowing thousands of additional warheads to penetrate and detonate on U.S. territory.

Former Air Force lieutenant general James A. Abrahamson, the SDI program's first director, strongly backed Cooper in a February 1989 memorandum to senior Pentagon officials, calling him "uniquely qualified. . . . at a critical time in the history of these defense programs."