President and Mrs. Ronald Reagan reached into establishment Washington yesterday to name Mabel Hobart Brandon, head of a public-relations firm dealing primarily in the visual arts, as White House social secretary.

The appointment of the 45-year-old Brandon, known as "Muffie" to her friends, ended a three month search among dozens of candidates competing for the prestigious position which will pay between $45,000 and $50,000 a year.

"We were looking for someone who was dynamic, imaginative and with Washington social savvy," said Peter McCoy, Nancy Reagan's chief of staff. Another essential was "chemistry," an ingredient First Lady Nancy Reagan is known to consider important in relationships with her staff.

Brandon's selection pointed up yet another effot by the Reagans to put down social as well as political roots in a town where they are stil newcomers. dEven before the Reagans had moved into the White House they began courting their new "neighbors" in Washington's business, cultural and social communities, in sharp contrast to their predecessors, Rosalynn and Jimmy Carter.

Brandon has played an active role in those three areas of Washington life and has been involved in the political community as a volunteer in the presidential comapaign of the late Robert F. Kennedy.

Acquaintances of Brandon yesterday praised her as the "qauintessential" insider who knows the nuances of Washington life first hand. She is married to a British citizen, Henry Brandon, chief diplomatic correspondent of the London Sunday Times. They live in Georgetown.

Since 1977 she has headed Washington Corporative Arts Inc., which she also founded. Before that, for two years, she was national director of the traveling Bicentential art exhibit "Remember the Ladies -- Women in America 1750-1815."

A 1957 graduate of Smith College, the alma mater of both Nancy Reagan and Barbara Bush, Brandon worked as assistant curator of New York's Riverside Museum from 1959 to 1960. Later, at Portland (Oregon) State College, she did graduate work in political science.

After moving to Washington, from 1963 to 1964 she was national coordinator for Project Headstart program in 300 rural counties.

Brandon said yesterday she was "honored and delighted" by her appointment, the last of the major East Wing positions to be filled by Mrs. Reagan.

"I think all events at the White House should reflect the excellence, the imagination and the creativity of the nation as well as the warmth and hospitality of President and Mrs. Reagan," Brandon said in a statement released by the White House.

Brandon's predecessor in the Carter White House, Gretchen Poston, yesterday called the Massachusetts-born appointee "very competent, someone who has all the qualities necessary to fill the job. And we're meeting for lunch tomorrow at the Jockey Club to celebrate. I'm going to offer her any assistance she might need."

Poston defined the role of White House social secretary as one of "translating the feelings and hospitality of the first family to its guests." Under the Carters, that hospitality often reflected their cultural interests as much as it did their Southern roots. Poston brought in such classical superstars as Vladimir Horowitz and Mstislav Rostropovich and such popular artists as Willie Nelson, Dolly Parton and Loretta Lynn.

Despite their eclectic cultural tastes, the Carters won little praise for their entertaining efforts. Veteran Washington observers still looked upon John and Jacqueline Kenndy as White House role models. In fact, Nancy Reagan turned to the Kennedy's first White House social secretary, Letitia Baldrige, to assist her in arranging the Reagans' first White House parties.

There's an atmosphere of the president and his wife that pervades Washington and spreads Out from there," said Lorraine Cooper, prominent Washington hostess who has been watching presidents and their wives come and go through the years.

"The Eisenhowers did things their way, they didn't entertain too much but they did all the traditonal things," said Cooper, whose husband John Sherman Cooper is a former U.S. senator as well as former ambassador to India and East Germany. "The way a president does things like that depends upon who the president's wife is."

How Nancy Reagan does things at the outset may depend to a great extent upon the White House social secretary. Commenting on Brandon's inside knowledge of Washington, a friend said the new social secretary could be "a real education" for the first lady.

Among Brandon's pulses, said the friend, are an easy familiarity with what's current and "right," and the "proper" social graces.

When Brandon was divorced from her first husband, journalist Eric Wentworth, her attitude was " We'll get throught this somehow -- keep our chins up," said Joan Bingham, a childhood friend from their years at Miss Porter's School in Farmington, Conn. "The main thing about Muffie is she's a Bostonian who believes in backbone and character. She mustn't worry about her Democrat friends thinking she's a turncoat."

At home, her entertaining style, according to her firends, is neither grand nor elaborate. As the mother of four, there isn't time for either.

"She's more interested in people than in the food -- not that the food isn't good," said Bingham.

Another friend described her seating combinations at dinner parties as "catalytic -- she really knows how to bring out the most interesting things in people." Said yet another friend, "If I were I man I'd love to have Muffie as my dinner partner. She's a superb conversationist."

Other well-connected Brandon friends reached yesterday were enthusiastic about her new position.

"That's a terrific choice," said Henry Kissinger, not only a friend but a frequent news source for Henry Brandon. Ironically, the British columnist was identified in the early 1970s as a journalist whose phone had been tapped by the U.S. government.Later, Brandon was involved in a brouhaha over published reports that President Nixon was once warned by J. Edgar Hoover that the columnist was suspected of working for British intelligence.

Another Brandon friend, Mary Henderson, wife of the British ambassador to the United States, said yesterday she was "thrilled" to learn of Muffie Brandon's new White House job.

"She's wonderfully efficient, with so charming a manner and knowledgeable about Washington. You need someone who knows Washington well and has lived here," she said. Of the effect fo Brandon's appointment on Ango-American ties, Henderson added: "They already exist without Muffie, but this will help."

In her capacity as head of an arts consulting firm, Brandon helped put corporations together with art exhibitions in need of sponsors. "She's been enormously helpful to us in obtaining corporate sponsorship," said Annemarie Pope, director of the Washington-based International Exhibition Foundation.

J. Carter Brown, director of the National Gallery of Art, where several of those exhibitions were held, called Brandon's touch "wonderful -- she has a feel for how to make it beautiful and also a feel for the human side of whom to invite and who should sit next to whom. Those are the more subtle sides and she has a real grip on it." Even her critics had to admit the first lady had made a good choice.

"Muffie's ambitious and a bit too much of a hustler for me, but she will subordinate herself until the time when she can put herself forward," one said. "Nancy Reagan is very lucky because Muffie knows her way around the city. So Nancy's got herself a plus rather than a minus."