We may never know what Frank Sinatra received for Christmas this year. But we do know at least one thing that he gave. For the 11th year in a row, a disabled 63-year-old great-grandmother, Eleanor Kopiasz, was the recipient of Sinatra's holiday generosity: The singer sent her 18 long-stemmed roses, a poinsettia plant and a fruit basket. Kopiasz, who lives in Buffalo with her retired husband, has in past years received a special mattress and a television set with remote control from Sinatra, who is said to admire her for her grit and determination. The two have never met.

Elsewhere on the gift-giving front: Books have been popular this season. Of course, it may help if you have a famous name to go with the book you're trying to sell. That's no problem for either Soviet leader Mikhail Gorbachev or real estate tycoon Donald Trump. Their respective tomes, "Perestroika" and "Trump: The Art of the Deal," have sold out in many stores across America.Queen for a Full Year

For Kaye Lani Rae Rafko, the 24-year-old nurse who happens to be the reigning Miss America, fulfilling all her regal duties can be exhausting. "At first, working 11 or 12 hours a day for five days straight, that was a little bit rough on me," she confided. So how does she manage to cope with her grueling schedule? "I remind myself it's only for a year." She added that if she accomplishes nothing else as Miss America, she wants to change the image of the pageant and its titleholder.

She also declined to work overtime in the Persian Gulf: Rafko turned down an invitation to travel there with Bob Hope because he could not guarantee that she'd be home by Jan. 3.

Rewriting Saroyan's Will

The will of author-playwright William Saroyan, who is best known for "The Time of Your Life" and "The Human Comedy," has been somewhat altered. The document had given the rights to his published and unpublished work to the San Francisco-based William Saroyan Foundation, an organization that awards grants to aspiring writers. His two children were left $170,000. But in a ruling last week in New York, federal court Judge Lloyd F. MacMahon turned over the copyright to Saroyan's play "The Cave Dwellers" to his surviving children, Lucy and Aram Saroyan. The writer severed relations with both children shortly before his death in 1981. Robert Setrakian, director of the foundation, said the ruling threatens the long-term existence of the organization, but an appeal has not yet been made.

A Christmas Wedding

In a Christmas ceremony in Israel, Oscar-winning actor Louis Gossett Jr. married an American soap opera actress -- Cyndi James Reese, who plays an undercover police officer in the television serial "Days of Our Lives." The ceremony was attended by a small group of family and friends.

Gossett, 51, has two sons: Satie, 13, from a previous marriage; and Sharron, 10, whom he adopted three years ago. The couple was married in a Baptist ceremony at a hotel in the resort town of Herzliyya, north of Tel Aviv. Gossett, who is in Israel to make a film, "Iron Eagle 2," flew in his aunt and 90-year-old grandmother for the wedding.

The Reagans' Christmas

After exchanging Christmas Day greetings yesterday by phone with their children, President Reagan and the first lady sat down to a sumptuous turkey dinner with 21 guests at the White House. The menu featured roast turkey with cornbread stuffing, roasted chestnuts, cranberry-orange relish, spiced acorn squash, pearl onions and peas, and a hazelnut mousse and meringue Christmas log.