The White House will announce today the complete list of appointees to its task force on the arts and humanities. It contains several surprise names, among them Nancy Hanks, the former chair of the National Endowment for the Arts, and Rawleigh Warner, Jr., chairman of the board of the Mobil Corp.

Along with Robert Fryer, artistic director of the Ahmanson Theatre in Los Angeles, these names are new to the list, under formation for weeks.

The task force will study the National Endowments for the Arts and the Humanities. Yesterday the endowments, in the latest round of the ongoing funding battle, were informed that recessions in their current budgets will be significantly less than expected.

In addition, any rescissions -- cutbacks in funds already appropriated -- proposed by President Reagan will not affect groups that had been tentatively promised funds, but had not yet received official notification signed by an agency chairman, endowment officials have been told.

Reagan is expected to recommend soon, as part of a message to be sent to Congress, that $6.65 million be rescinded from the NEA and $7.417 million from the NEH in each agency's fiscal 1981 appropriations. These figures are significantly less than the originally expected recissions of $15 million in outlays for each agency. NEA officials had translated that figure into about $30 million in appropriations.

Altogether 32 people, plus three co-chairs and the vice chairman, will be on the task force, which includes Washington members Daniel Boorstin, librarian of Congress; Leonard Silverstein, president of the board of the National Symphony Orchestra; and Roger Stevens, head of the Kennedy Center. Last month, the White House announced the co-chairs -- actor Charleston Heston, University of Chicago President Hanna Gray, and Daniel Terra, ambassador-at-large-designate for cultural affairs. Barnabas McHenry, the general counsel to Reader's Digest, was named vice chair.

In the last few weeks, Nancy Reagan has become involved in the selection of the task force, according to sources. "She wanted three more names for the list," said one source earlier this week.

Hanks, long considered a respected and powerful advocate for the arts in Washington, has not been very involved with the Reagan administration in the area of the arts until now.

"I am honored to serve," said Hanks, who was only recently asked to join. "I believe very strongly in private support of the arts. I also believe strongly in public support of the arts. I think the task force will provide a good airing of views."

Mobil's Warner serves as chairman of the Business Committee for the Arts, a national organization that promotes corporate support of the arts.

Although the task force has not yet met, Heston seems to have already effected soem change by telling White House officials that he felt the expected recission in federal funds this fiscal year to the NEA was "unwise."

Initial estimates, made several weeks ago, shocked arts organizations nationwide that were expecting grants. Many had borrowed money and made touring arrangements based on expected funds -- only to be left in limbo while the endowments tried to figure out how to cut back.

"We plan to meet all the commitments we've made," said NEH chairman Joseph Duffey, who confirmed that he had been informed unofficially of the revised rescission figures. "It won't be necessary to cancel commitments." Duffey added that the freeze on NEH grants had been lifted last week.

NEA chairman Livingston Biddle had no comment on the new figures. He did confirm that he had provided documentation to OMB and to the White House task force representatives on how NEA notifies grantees. "I emphasized . . . that when the panel meets and the [National Council on the Arts] meets and approves funding, the applicant is informally but quite emphatically told that the money is approved."

Other members of the White House task force on the arts and the humanities include:

Margo Albert, actress and National Council on the Arts member;

Edward C. Banfield, Harvard University government professor;

Anne Bass, Fort Worth, Tex., arts patron;

William Bowenk Princeton University president;

Joseph Coors, president of Adolph Coors Co., brewery, in Golden, Colo.;

Armand Deutsch, California industrialist;

Virginia B. Duncan, Bechtel Corp. executive and former television producer of San Francisco;

Henry Geldzahler, commissioner of the New York City department of cultural affairs;

Gordon Hanes, chairman of the board of the Hanes Corp. of Winston-Salem, N.C.;

Paul R. Hanna of the Hoover Institution at Stanford, Calif.;

Ernest J. Kump, architect;

June Nobel Larkin, of the Edward John Noble Foundation in New York City;

Robert Lumiansky, president of the American Council of Learned Societies;

Angus MacDonald, president of the Angus MacDonald Co. and founder of the Massachusetts Institute of Technology Council on the Arts;

Nancy Mehta, wife of conductor Zubin Mehta, and former vice-president of the 400 Group of the Los Angeles Music Center;

Arthur Mitchell, founder and co-director of the Dance Theatre of Harlem;

Franklin Murphy, chairman of the board of Times Mirror Co. in Los Angeles;

David Packard, chairman of the board of Hewlett-Packard of Palo Alto, Calif.;

Edmund Pillsbury, director of the Kimbell Art Museum in Fort Worth, Tex.;

George C. Roche, president of Hillsdale College in Hillsdale, Mich.;

Richard Mellon Scaife, chairman of the board of the Tribune Review Publishing Co. in Pittsburgh;

Franklin Schaffner, film director;

Beverly Sills, opera singer and director of the New York City Opera Company;

Robert I. Smith, president of the Glen Meade Trust in Philadelphia;

John Swearingen, chief executive officer of Standard Oil;

Lucien Wulsin, chairman of the Colorado Council on the Arts and Humanities and chief executive officer of Baldwin United Corporation, Denver.