Japan's newly elected prime minister, Yasuhiro Nakasone, today named veterans from the ruling Liberal Democratic Party to key Cabinet posts, including a number of controversial appointments, amid a public outcry that threatened his administration with a stormy start.

In announcing the country's new political roster, Nakasone packed top government and party jobs with powerful proteges of former prime minister Kakuei Tanaka, leading to accusations that he has helped to bolster Tanaka's shadowy role in Japan's national affairs.

Tanaka is on trial in the six-year-old Lockheed bribery scandal, and was forced to resign his membership in the ruling party after his indictment. But he continues to control by proxy the conservative, largely pro-American party's biggest parliamentary faction, which strongly supported Nakasone in his bid for the premiership.

"This is not, in fact, a Nakasone Cabinet, but a Tanaka Cabinet," said political commentator Takasi Tachibana, reflecting the belief here that Tanaka is maneuvering behind the scenes to ensure his political survival beyond a court ruling in the Lockheed case that is expected sometime next year.

Nakasone was forced to delay the announcement of his new Cabinet until late tonight because of the embittered response of ex-premier Takeo Fukuda, who leads a rival wing of the party that strongly opposed Nakasone's bid. Members of Nakasone's own faction reportedly also were angered by being passed over for important government jobs.

Nakasone was named prime minister early today in a special session of the LDP-dominated Diet, Japan's parliament, following his landslide victory Wednesday in primary election for president of the party. He succeeds Zenko Suzuki, who unexpectedly announced on Oct. 12 that he would step down in the midst of factional infighting.

In the ensuing six-week campaign, Nakasone stressed the need to strengthen ties with the United States, which have been badly strained by a huge U.S. trade deficit with Japan and Washington's demands that Tokyo move more quickly to boost its modest defense budget. Reports in the Japanese press today said that Nakasone intends to visit Washington in January for talks with President Reagan.

Political analysts feel that Nakasone may have damaged his apparent mandate from the voters by favoring Tanaka loyalists so heavily in his new Cabinet. In his most controversial appointment today he named Masaharu Gotoda to be chief Cabinet secretary, the top government spokesman. Gotoda, 68, a former career bureaucrat in Japan's national police force, is reputed to be the key figure in Tanaka's brain trust.

The move represents a sharp break with Liberal Democratic Party traditions that call for a prime minister to name a Cabinet secretary from his own faction in the Diet. Nakasone's parliamentary faction is the fourth largest in the LDP, which has had a monopoly on power here for the past 27 years.

In another key appointment, Nakasone named Akira Hatano, a political independent believed to have close ties with Tanaka, to head the Justice Ministry. Hatano, 71, is a former superintendent general of Tokyo's police who touched off a furor recently when he criticized public prosecutors for their handling of the Lockheed case.

Noboru Takeshita, 59, who is thought to be the heir-apparent in Tanaka's Diet faction, was made finance minister, bringing the number of Tanaka's followers on Nakasone's 20-man Cabinet to six. Four Tanaka loyalists served under former prime minister Suzuki.

In a related move, Susumu Nikaido, 73, was reappointed to serve as LDP secretary general, an influential post that controls the party's purse strings. Nikaido, a senior member of the Tanaka faction, was implicated but was not indicted in the Lockheed case.

Nakasone rejected allegations that Tanaka influenced his choice of Cabinet ministers, reportedly saying he awarded the portfolios to put "the most capable men in the most responsible positions."

In an apparent bid to balance factional representation in his Cabinet, Nakasone gave the job of foreign minister to Shintaro Abe, 58. Abe, widely viewed as a prime candidate for a future premiership, belongs to the faction headed by Fukuda and ran a distant third in the primary.

In other appointments, Sadanori Yamanaka, 61, was tapped to head the powerful Ministry of International Trade and Industry and Kazuo Tanikawa, 52, became director general of the Defense Agency.