Apparently moving to quell a rising revolt among conservative whites against South Africa's policy in Namibia (Southwest Africa), Prime Minister Pieter W. Botha today announced the appointment of Gerrit Viljoen, reputed head of the secret and powerful Broederbond society, as administrator of the territory ruled by this country.

Viljoen, now rector of Randse Afrikaanse University here, will take over from the sometimes abrasive Marthinus steyn, who will return to his former job as judge in the province of Orange Free State.

Steyn's departure is not expected to affect renewed Western initiatives to break the impasse in negotiations with South Africa over a United Nations plan to bring Namibia to a peaceful independence. The plan calls for a cease-fire in the 13-year-old war between South Africa and its guerrilla opponents, the Southwest Africa People's Organization (SWAPO.)

If Botha and his new surrogate Viljoen fail to assuage the conservative whites anger, however, a serious revolt in Namibia could spill over into South Africa, where Botha's party is alrejdy in internal turmoil. This could force Botha to take a much harder line in future negotiations with the Western countries.

A new round of talks on the plan will begin in mid-August when British envoy Sir James Murray comes to South Africa as the official spokesman for the five countries engaged in the negotiation -- the United States, Britain, France, West Germany and Canada. Britian, with a Conservative government more sympathetic to South Africa, will thus take over the role once belonging to the United States in the person of the deputy ambassador to the United Nations, Donald McHenry.

The U.N. plan Lost momentum in March when South Africa objected to its implementation. Since then, SWAPO guerrillas have increased their activities in the traditional "operational" area along Namibia's border with Angola, where they have sanctuary. They have also struck deep into the normally peaceful areas in central Namibia, killing a number of white civilians -- a rare occurrence in this war, in contrast to the conflict in Zimbabwe-Rhodesia.

SWAPO, which once was permitted to operate as a political party inside the territory even while its external wing carried on a guerrilla war, has has to disband its overt political activities because of police harassment. Its office in the capital, Windhoek, is now closed and latest newspaper reports said that 72 members were still in detention without charge under South African security legislation.

In addition, the right-wing backlash has become violent. In one incident. a grenade was thrown into a Free mason meeting, killing one white man and wounding others. Two white men have been arrested for the attack.

As head of the Broederbond, the secret organization of Afrikaner men that is the power behind the scenes in South Africa's ruling National Party, Viljoen is a "political heavy-weight," according to one analyst. He favors moderate change here and thus is squarely in Botha's camp within the party.

Botha appears to hope that Viljoen's prestige and tadtful personality will help him persuade the conservative whites to cease their public squabbles with the moderate whites of the territory -- whose alliance with blacks in the Democratic Turnhalle Alliance is backed by Botha's government.

Attacks by Namibian right-wing leader A.H. Duplessis on the alliance's chief, Dirk Mudge, have embarrassed the government here. Duplessis' activities became a matter of concern when it appeared that his faction was not only gaining support among whites of the territory but was also covertly lobbying for support among opponents of Botha in his own party inside South Africa.

Whites in Namibia number about 91,000. About 70 percent are Afrikaans-speaking South African citizens. The conservatives among them object to the introduction of universal suffrage in a territorial election last December and to what they call "forced integration" under a new law that make it a crime to discriminate on grounds of race in residential areas and public facilities.

The Botha government is urging the whites of the territory to accept changes it is not yet prepared to make in South Africa.

Duplessis recently threatened to lead a column of discontented whites into South Africa if the trend continues. The South Africans are concerned that a massive outflow of whites would leave the civil service weakened and thus sabotage their efforts to build up the moderate Turnhalle Alliance into a popular, effective alternative to the socialist inclined SWAPO for any future internationally supervised election. CAPTION: Map, no caption, By Dave Cook -- The Washington Post