After a one-day search, First Lady Nancy Reagan yesterday reached into her own back yard and named Gahl Hodges, a 29-year-old Washingtonian, as White House social secretary.

Hodges, currently assistant chief of protocol, will replace Mabel (Muffie) Brandon, who resigned her post effective June 1 to become president of a newly established office of a public relations firm.

"I just heard about it," said Hodges from the White House last night. "I'm very excited and thrilled. I still can't believe it."

Hodges said she was first approached Tuesday by White House Deputy Chief of Staff Michael Deaver, who is particularly close to Mrs. Reagan. Deaver asked Hodges to meet with the first lady later in the day.

"Well, Mrs. Reagan talked about how she liked her staff to portray her personal desires and wishes," said Hodges. "And we talked about my previous job in the office of protocol. We talked about how she views the job of social secretary. She, of course, was very complimentary to Muffie Brandon and wants me to work closely with Muffie to see how things are done."

James Rosebush, Mrs. Reagan's top staff aide, said Hodges would come to the White House next Monday and begin working with Brandon "on a part-time basis."

"Everyone thought of Gahl immediately when this came up," said Rosebush. "We had worked with her . . . Everyone beamed when her name came up."

Most recently, Hodges worked closely with the social office during Queen Elizabeth's visit to California, although she only met Mrs. Reagan for the first time Tuesday.

When the Reagans first came to Washington, Brandon was selected after a three-month national search.

Essentially, the White House social secretary is a behind-the-scene organizer for fancy parties. Along with the first lady, she picks the flowers, the tablecloth colors, and decides whether it will be veal or chicken and who will be invited to eat it.

In this administration, the social secretary also works with Frank Sinatra on the entertainment for state dinners.

Rosebush said yesterday Hodges had competition for the job, but he declined to name names. He also said "others" were interviewed by Mrs. Reagan before she selected Hodges.

Born in Washington, Hodges was raised in Cocoa Beach, Fla. She earned an associate of arts degree from Wesley College in Dover, Del., and served as a State Department protocol officer from 1979 until last February, when she was named assistant chief of protocol.

Before 1979, she served as a personal assistant to secretaries of state Henry A. Kissinger and Cyrus R. Vance.