Less than a week after the funeral of the late Rep. Joseph P. Addabbo (D-N.Y.), 42 of his colleagues in Congress have applied for the prime office space he occupied in the Rayburn House Office Building.

Office space on Capitol Hill is distributed according to seniority, and Addabbo, a 15-year veteran and chairman of the Appropriations defense subcommittee, is said to have occupied choice real estate. The 20 members of his staff will stay at least until a new member of Congress is elected for the Queens district Addabbo represented, but they have been assigned new quarters for the time being.

Negotiations over the prize are handled by the office of the Architect of the Capitol. Spokesman Elliott Carroll told States News Service, "They don't wait until the body is cold. But that's politics, I suppose." Down on the Farm? . . .

In the weeks since Frank W. Naylor Jr. was nominated to be chairman of the board of directors at the Farm Credit Administration, speculation has been rife about who will succeed him as undersecretary of agriculture for small community and rural development -- the part of USDA responsible for development and credit programs, including the Farmers Home Administration.

Kathleen W. Lawrence, who was Naylor's chief aide, now looks like Agriculture Secretary Richard E. Lyng's probable choice -- news that has Sen. Charles E. Grassley (R-Iowa) up in arms. Grassley is up for reelection this fall, and the farm crisis could be a major political liability. As Naylor's aide, Lawrence has spoken on many Reagan administration farm credit policies that have angered farm-state Republicans and brought charges of insensitivity. In addition, most of her experience before 1982 was in political campaigns, not in agriculture or finance.

Grassley is circulating a letter among fellow senators, seeking signatures for a plea to the president that someone be appointed who "has a strong agriculture and farm finance background -- a rural American . . . . " But he may run up against a political imperative of another kind: Lawrence's appointment would make her the highest-ranking woman in the history of the traditionally male-dominated department. Gamesmanship . . .

The Bureau of Indian Affairs, reversing a longstanding policy, is notifying leaders of Indian tribes that it wants to review any contracts granted to outside companies to run bingo games.

Tribal bingo games are wildly popular and profitable because they have been exempted by tradition, and recent court rulings, from state gambling regulations. Interior Secretary Donald Hodel has defended them on grounds that they may provide the only jobs on reservations where unemployment is high. But increasingly, bingo is subcontracted to companies from outside the reservations, causing concern about an unintended form of legalized gambling.

Between 105 and 110 tribes are running bingo games, said Vince Lovett, spokesman for the bureau. But it is not known in Washington how many tribes have hired outsiders to manage the games or how many of those contracts have been approved. Nominees . . .

President Reagan plans to nominate A. David Rossin, an official of the Electric Power Research Institute in Palo Alto, Calif., as an assistant secretary of energy, the White House said Friday.

The announcement said Rossin would be named assistant secretary for nuclear energy. Since 1981 he has been director of the Nuclear Safety Analysis Center of the Nuclear Power Division of the institute.

The White House also said Reagan plans to nominate R. Kenneth Towery, president of the Sentinel Corp., a business and political consulting firm in Austin, Tex., as a member of the Corporation for Public Broadcasting.