The name of one of Nancy Reagan's deputy press secretaries was incorrectly given in yesterday's Style section. She is Barbara J. Cook.

"After I was flown back from Vietnam, the doctor said I had a choice--I could lie there on my back and be miserable, or I could find something to occupy myself. So I took up needlework," said Arthur Seippel. "The other men in the ward ribbed me about it until they saw how much extra attention and food I got from the nurses."

He explained this as he stood with his cane in the upstairs bedroom of Woodlawn Plantation, surveying the quilt entries of the 20th annual Woodlawn Needlework Show. Seippel, who has won several ribbons in his 12 or so entries over the years in the exhibit, didn't enter this year, "because we just finished stitching 24 kneelers for our church in Winchester, Virginia."

About 700 other needleworkers from 34 states and four foreign countries entered 1,200 pieces--gros and petit point, counted-thread work, crewel, applique', quilting and so-called creative stitchery, among other techniques. All entries are on exhibit through Sunday; from Monday through April 3 only the ribbon winners will be on view. The plantation is south of Mount Vernon at Rte. 1 and Mount Vernon Parkway.

The show annually grosses about $100,000 as a major support of Woodlawn. The house was designed by early Washington architect William Thornton about 1800 for the wedding of George Washington's adopted granddaughter Nelly Custis and his nephew Maj. Lawrence Lewis. Custis was noted for her needlework.

On the opening days, men and women lined up to wander through the classic Georgian house, admire the needlework spread over the antique furniture, observe the crocus and tulips poking through the ivy, and eat sandwiches in the 19th-century pub in the basement.

"This year we have more needlepoint rugs, counted thread and quilted work than ever," said Margaret Davis, who is retiring this year after directing the show for the last 17 years. "But creative stitchery and crewel work are almost extinct. There are fashions in stitchery techniques as in everything."

One needlepoint rug promised for the VIP exhibit wasn't finished in time; Barbara Bush, the vice president's wife, called up to say she had been too busy to finish it.

Another needlepoint rug, worked on for three years by 75-year-old J. Gordon Ramsden of Pittston, Pa., was named the best-in-show. A geometric design with elaborate shading by Alexander Breckenridge of New York was judged the most original. Other top honors were won by Mary Ellen Sandlin of Arlington for a Ghiordes knot stitch rug and Jennifer Cherry of Lothian, Md., for a sampler.

Barbara Eisenhower, the daughter-in-law of the late president, sent in the Christmas stocking made for her grandson Alex. A copy of the needlepoint upholstered stool Nancy Reagan sent to Britain's Prince William, infant son of Charles and Diana, was there. Not to mention a bargello pillow Lucinda Robb made for her grandmother, Lady Bird Johnson; and two pillows with designs copied from White House china of the John Adams and James Monroe period worked by Barbara J. Cox, deputy press secretary.

"I like to look," said one woman, "but I don't have the patience to do this sort of thing."