Nancy Hanks, with customary wit, used to brag that she was named after a famous race horse. But last night, at a preview of The Pavilion, the three-story section of The Old Post Office that is scheduled to open next summer, the conversation was about naming the nearly completed renovation in honor of Hanks. The former chairman of the National Endowment for the Arts died Jan. 7.

Robert Peck, an aide to Sen. Daniel Patrick Moynihan (D-N.Y.), said last night that a meeting has been scheduled for Thursday by Sen. Robert T. Stafford (R-Vt.), chairman of the Senate Committee on the Environment and Public Works, to discuss whether to call the building the Nancy Hanks Building or to call the performing arts area at the foot of the clock tower the Nancy Hanks Center at The Old Post Office.

Peck said such legislation is expected to be introduced when Congress reconvenes next Tuesday. Supporters hope it will pass in time for a memorial service for Hanks scheduled in Washington Feb. 2.

But there were differing views on how she should be memorialized. George White, architect of the Capitol, said, "I am in general not in favor of naming buildings after people who've just died. But if there is an exception, it would be Nancy Hanks."

Arthur Cotton Moore, architect of the renovation of The Old Post Office, said he thought it was better to keep the current name, because it is a part of the city's history, and to name the stage area after Hanks. D.C. City Council member Polly Shackleton said she thought there should be some memorial to Hanks in the building. Peck said that on the Monday after Hanks' death Moynihan's office received 50 letters suggesting that The Old Post Office be named for her.

Frank Hodsell, current chairman of the NEA, said he understood that there was considerable sentiment for the proposal. Various speakers on the program last night paid tribute not only to Hanks, but also to the concept of the building renovation. Hodsell said he and the rest of staff at the NEA and the National Endowment for the Humanites expect to move into their new space in the building by the beginning of April. Last night, he took his wife, Mimi, to have the first look at what will be his new office on an upper floor.

The program, which went on for more than an hour, included speeches by Charles C. G. Evans Jr., developer of The Pavilion; Benjamin Thompson, The Pavilion's architect; Craig Claiborne, food editor of The New York Times; fashion designer Ronald Kolodzie (who introduced a show of his own fashions), and jazz pianist Billy Taylor. After each speech, a new segment of the audience left for the cortile, where 12 restaurants were serving such delicacies as pecan cheesecake, barbecued spare ribs and chicken and crab salad with green sauce.

The auditorium, the one warm room in the cavernous, unfinished space, was full at the beginning of the program. When the time came for the last three speakers -- Hodsell, Max N. Berry, chairman of the Pennsylvania Avenue Development Corp., and Gerald P. Carmen, head of General Services Administration -- there was hardly anyone left in the audience. By general agreement, the last speeches were not given and everybody from the platform went out in search of a drink and a few leftovers.

The Old Post Office has been threatened for most of its life with demolition because it doesn't match the classic revival architecture of the rest of the Federal Triangle. Don't Tear It Down, a preservation group, was organized and effectively protested its demolition about a decade ago. But the key to saving the building was Hanks' campaign to have it renovated.

The plan she proposed in February 1974, after a study headed by Bill Lacey, then head of the NEA's architectural section, was to make offices on the upper floors for the Endowments with restaurants and shop facilities below for the public. The proposal was one of the first for mixed public and governmental use.

"My plan for the building was to make it as a link between the federal capital of museums and offices and the city of Washington on the other side of the gulf of Pennsylvania Avenue," said Moore, looking at the still unfinished lower floor.

Most of the visitors seemed to agree that the building itself, a fantastic Romaneseque Revival structure built in 1899 to a design by Willoughby J. Edbrooke, is awesome. The sensational cortile, or interior court, is 10 stories -- 196 feet high -- with 90 by 184 feet of floor space a glass roof. The other floors form balconies around the cortile. The main floor was originally the mail sorting room with a catwalk above it that inspectors used to check on the honesty of the sorters.

The 60,000-square-foot retail center, patterned after European arcades, is expected to have 25,000 square feet of specialty shops on the lower level, 23,000 square feet of restaurants and shops on the main floor and another 12,000 square feet of restaurants on the balcony level.

Thompson, who designed Boston's Faneuil Hall Marketplace, which has a number of places to eat, once said he started that project so he'd have a decent place to eat near his office.