Nancy Reagan says her son, Ron, is "very conscious" about not wanting to trade on the family name in his pursuit of a career as a ballet dancer.

"If a paper wants an interview just with him, he'll always say 'with the whole company,' or if they want a picture of him, he'll say 'with the whole company,' " Mrs. Reagan told Arlene Francis, the host of WNBC-TV's "Prime of Your Life" show, during a taping session here today. The show will be aired in the New York area in two segments, on Nov. 13 and Nov. 20.

The first lady said she was not surprised when young Reagan was laid off last month by the Joffrey Ballet because she knew that most ballet companies have a month's layoff.

"He had been with Joffrey II and he had just signed with Joffrey I when the layoff came. If he had waited another month to sign, he'd have been all right," she said.

Reagan and 40 others in the Joffrey's principal company went off unemployment compensation this week when they resumed rehearsals this week for "The Taming of the Shrew," scheduled to open Dec. 22 in New York City.

"I was very proud of him. We offered to help him and he said no -- 'No, I don't want your money. I'm going to do what everybody else does in the company.' "

Francis called young Reagan's rejection of help "first-class behavior -- I think most people would have felt he could always get help."

Mrs. Reagan also told Francis that becoming first lady had brought tasks she was not prepared for -- "I didn't know it would be that demanding." She misses her friends, she said, and she also misses her dogs, which are kept at the Reagans' California ranch.

"We have a lot of them. A lot of strays are thrown out of cars, and I think the word passed around that ours is the place to go," she said, laughing. "Our dogs are used to wandering in and out of the house at will and that's a little hard to do in that house the White House . I miss reaching down and patting a little head."

When Francis suggested she have a dog in Washington, the first lady voiced some reservations.

"How would it go in and out?" she asked.

Mrs. Reagan returned to Washington this afternoon, winding up a two-day trip to promote her book, "To Love a Child," about the Foster Grandparents program. After a publication party Wednesday evening at Lincoln Center, she went on to a private dinner given by Pat Buckley, wife of colummnist William F. Buckley. Other guests included designer Bill Blass; socialite Nan Kempner; columnist Aileen Mehle; songwriter Joshua Logan and his wife, Netta; and Ron and Doria Reagan.