Alfred S. Regnery is stepping down after 3 1/2 controversial years as head of the Office of Juvenile Justice and Delinquency Prevention. Regnery's relations with some Justice Department officials were so strained, sources said, that his immediate supervisor, Assistant Attorney General Lois Herrington, did not know about his departure until the news was leaked to The Washington Times.

Since weathering stormy Senate confirmation hearings in 1983 that focused on his reputation as a juvenile justice hardliner, Regnery has espoused the Reagan administration belief that his $70 million grant-giving office should be abolished. Congress, however, has been loath to cut off funding to runaway centers and drug clinics.

Regnery recently made headlines when he awarded a $186,710 grant to conservative activist James McClellan and a dean at Jerry Falwell's Liberty University to write a course on the Constitution for high school students. The award drew bipartisan protest because it came at a time when all other grants from Regnery's office were frozen as part of the administration's attempt to get rid of it.

Regnery's most famous grant was a $734,000 award to Judith Reisman, a fervent opponent of pornography and former songwriter for Captain Kangaroo, to perform a "content analysis" on Playboy and Penthouse magazines. Regnery has defended the study as important to research on child exploitation, but he will leave office June 6, shortly before the study is to be released. Regnery will join the law firm of Mayberry, Leighton and will open a Washington office for his family's publishing company. Joint Announcement . . .

As expected, President Reagan yesterday nominated Adm. Carlisle A. H. Trost, commander of the Atlantic fleet, to become chief of naval operations, and Gen. Larry D. Welch, who now heads the Strategic Air Command, to be chief of staff of the Air Force.

If the two men are confirmed as easily as expected, Trost will be taking over from Adm. James D. Watkins, and Welch from Gen. Charles A. Gabriel, whose terms end June 30. Tower of Power . . .

The public relations firm Gray & Co. has announced that former senator and Armed Services Committee chairman John G. Tower (R-Tex.) has been elected to its board of directors. Tower retired from the Senate in 1985, and has since worked in Geneva as a U.S. negotiator on strategic nuclear arms.

Gray & Co. Chairman Robert Keith Gray noted in a release that Tower's "many years of congressional experience in defense and budget affairs will further enhance our team of advisers," who counsel such clients as the embassies of South Korea and Turkey. Final Inspection . . .

The Pentagon yesterday announced the retirement of inspector general Joseph H. Sherick, the Defense Department's point man in the war against errant contractors.

Defense Secretary Caspar W. Weinberger released a statement praising Sherick, saying, "His efforts have resulted in billions of dollars of savings for the Department of Defense." And a Pentagon spokesman said Weinberger was awarding Sherick the department's Distinguished Public Service medal. A Lawyer Joke . . .

Speaking at a Harvard Law School Association luncheon Tuesday, Supreme Court Justice William J. Brennan Jr., class of '31, took the opportunity to rebut one of the arguments against broadcasting arguments at the high court. Chief Justice Warren E. Burger has objected that if the court permits radio and television coverage, networks would run snippets of the arguments instead of airing them in their entirety. "Thank goodness," Brennan responded. "I think some of the lawyers who argue those cases will be just as happy we don't."