There will be two staffs, in effect, handling the public and private lives of Rosalynn Carter and the Carter family when they take up residence in the White House Jan. 29, the Carter-Mondale transition office announced yesterday.

One staff, dealing with Mrs. Carter's public activities, will be coordinated by Mary Finch Hoyt, 52, Washington journalist, author and public relations executive who has been named president secretary to the first lady and east wing coordinator.

That staff will include newly-named White House social secretary Gretchen Poston of Washington and six other aides, among them deputy press secretary Ann Anderson, 40; appointments secretary Jane Fedsrson, 34; director of projects, reserach and issues Kathy Cade, 29, and east wing writer Coates Redmon, 45.

Madeleine MacBean, 39, of Atlanta, who was personal secretary to Mrs. Carter when Carter was governor of Georgia, has been named personal assistant to the First Lady.

"I'll be dealing with the public Rosalynn," said Hoyt, who served as Mrs. Carter's press secretary during the campaign and, later, the transition, "and Madeleine will be handling the private Rosalynn."

Although Mrs. Carter will maintain a permanent office in the East Wing of the White House where she personally will direct her 18-member staff, Hoyt said that she will be responsible for providing liaison with the President's West Wing staff.

Ministering to the needs of Rosalynn and Jimmy Carter's family living in the White House which in addition to Amy will include sons Chip, 26, and Jeff, 24, and their wives, will be a staff of five.

They include one man, Rikc Hutto, named family appointments secretary, and four women - Helen Dougherty, personal secretary and director of correspondence; Rita Merthan, corresponding secretary; Carol Benefield, administrative aide, and Wanda Davis, family secretary.

The Carter sons and their wives will occupy two apartments on the third floor of the executive mansion, quarters currently occupied by Jack and Susan Ford, a transition spokesman said. President-elect Carter has previously announced that son Chip, whose wife Caron, 25, is expecting a child in March, will serve as a presidential emissary on occasion. The personal staff to the Carter family will handle arrangements for such missions, the spokesman said.

Rosalynn Carter reached into the ranks of her husband's campaign staff for several appointments, but in the case of Gretchen Poston she turned to campaign volunteers of Vice President-elect Walter Mondale.

A partner with Ellen Proxmire and Barbara Boggs in the highly successful convention-planning business called Washington Whirl-Around Poston had been proposed for the White House position by "several sources," according to Hoyt. Mrs. Carter took it under serious consideration during a recent stay at St. Simon's Island where she consulted Joan Mondale, a longtime friend of Poston's.

Married to Washington attorney Raymond Poston and the mother of four children, Poston said yesterday that for a White House social secretary-to-be she has the distinction of never having been invitied to a White House dinner or a White House luncheon.

Mrs. Carter's other staff choices reflect her special area of interest - mental health - and indicate a determination to actively focus nationwide attention on it.

Cade, a native of Montreal who becomes director of projects, research and issues, was a coordinating producer of WNET in New York, working specifically in health area programming.

Coates Redmon of Winston-Salem, N.C., who becomes East Wing staff writer, produced "Feeling Good," a health program for children's television workshop in New York.

At least three of her staff - Hoyt, Anderson and Redmon - are Peace Corps "alumnae," where they first became acquainted. Anderson subsequently has written on consumer-protection issues, gardening and food for The Washington Post and Washingtonian magazined. She is married to jimmy Carter speechwriter Pat Anderson.

Hoyt is the author of two books, one - "Uphill - A Personal Story" - in collabration with Eleanor McGovern - for whom she was press secretary in George McGovern's 1972 campaign for President.

Hoyt served in a similar capacity to Jane Muskie when Sen. Edmund S. Muskie briefly sought the Democratic nomination for president in 1972.

Hoyt's press office staff will be rounded out by Barbara Heineback of Albany, Ga., a free- lance journalist named Press Advance, and by Faith Collins of Boston, Press Assistant.