Linda Faulkner, a Dallas public relations executive, will succeed Gahl Hodges as White House social secretary, Nancy Reagan's office announced yesterday.

Faulkner, 35, who was deputy social secretary at the White House for the first three years of the Reagan administration and worked under her predecessor for 10 months, will start work in the $55,700-a-year post Sept. 2.

She was rumored as Hodges' successor after Hodges' husband, Assistant Secretary of State Richard Burt, was nominated to be U.S. ambassador to West Germany. He is awaiting Senate confirmation.

Yesterday, Faulkner said she had been approached about the job some time ago and since then had been quietly dissolving the public relations firm she started in January 1984, when she returned to her native Dallas from Washington.

She said she has not been back to Washington since then, but that Mrs. Reagan telephoned her recently "to tell me how glad she was that I am coming back. It's very comforting to be wanted, though I know that she has loved Gahl. I only hope I can do as good a job."

Faulkner came to the attention of Nancy Reagan in 1980 when longtime friend and Washington lobbyist Nancy Reynolds was helping put together a White House staff for the first lady. Reynolds learned of Faulkner from Letitia Baldrige, White House social secretary during the Kennedy administration.

Faulkner said she was working in public relations at Neiman-Marcus' downtown Dallas store when she first met Baldrige, who had come to town to promote her book, "The Amy Vanderbilt Complete Book of Etiquette."

"We sort of kept in touch and later we asked her to come back to Dallas to work on the Neiman-Marcus Creative Entertaining Seminar in the spring of 1980," Faulkner said.

A self-described "good Republican, though I never actually worked on the (Reagan-Bush) campaign" in 1980, Faulkner said she always thought it had been a "phenomenal opportunity" to work at the White House during Reagan's first term in office.

"I admired the Reagans tremendously. I remember thinking, 'If I had my choice of presidents, this would be the one I'd choose.' Now, what an honor to be going back. I'm so excited," Faulkner said.

A graduate of Vanderbilt University, where she majored in philosophy, Faulkner worked at Penn Resources Inc., an oil and gas corporation, and was a production assistant and an assistant director of KERA-TV, a Dallas public broadcasting station.