White House chief of staff Donald T. Regan has at least three names on his desk as finalists for Linda Chavez's job of deputy assistant to the president for public liaison.

They are Judy Wiedemeier, currently a lobbyist for the tobacco industry; Karlyn Keene, resident fellow and managing editor of the American Enterprise Institute's Public Opinion magazine; and Nancy J. Risque, special assistant to the president for legislative affairs.

Wiedemeier's strength is that she was an early (1976) Reagan supporter; Keene's that Pat Buchanan, White House director of communications, reportedly supports her; and Risque's that she already has a White House pass.

Did Lucky Reagan, the 65-pound Bouvier des Flandres sheepdog whom the Reagans gave the bum's rush by exiling to their California ranch, also get a bum rap?

One of the country's top trainers, who has trained pooches for dozens of famous people, says that from watching television footage of Lucky pulling Nancy Reagan across the White House lawn he thinks improper handling as much as Lucky's rambunctious nature contributed to her fall from grace.

"Mrs. Reagan should have given the dog a leash correction and told her to heel," says Capt. Arthur Haggerty of New York and New Jersey, whose pupils have included Brooke Shields, Cliff Robertson, John Huston, Flip Wilson, Liza Minnelli, Rodney Dangerfield and their dogs.

To have given Lucky a correction like that, Mrs. Reagan would have had to go through obedience training sessions with the dog. Sources say neither the first lady nor the president had time for such instruction even though Lucky's trainer, Bob Maida of Manassas, repeatedly recommended it.

Most of Lucky's handling, sources say, was by White House maintenance staffers. Unlike Rex, the new First Pooch who sleeps in the Reagan bedroom, Lucky slept in the engineer's office.

According to Haggerty, that's like leaving Lucky in the care of the maid, butler or chauffeur. "I always refuse to work with them because they're apt to see the dog as an added chore and think negatively rather than positively about it."

Can any First Couple find happiness with a dog in the White House? Haggerty concedes that it's a unique situation.

"If you ask me, 'Does the president of the United States have time to put in working with his dog?,' I'd say, 'Probably not.' But if he's really interested in his dog and decides to give it even 10 or 15 minutes a day, it will work out," Haggerty says.

As a breed, the choice of a Cavalier King Charles Spaniel, sometimes called "an ornamental dog," was a good one for Mrs. Reagan, who doesn't have "too good a hand" with a dog, Haggerty says.

"You can get away with a poor hand with a Cavalier easier than with a Bouvier. Even if Lucky had been small like Rex, Lucky would have required more handling because Bouviers are bred for hard work."

*And most days around the White House, it was a dog's life.

If Lucky is a has-been, Rex is just beginning to find out what it means to be famous. A long-eared black and white stuffed First Pup called "Rex" was unveiled at the New York Toy Fair last week. He's outfitted with a collar bearing his name and address (1600 Pennsylvania Ave.) and comes with his own pedigree papers. Optional accessories include a red monogrammed sweater and even the proverbial silver spoon in the shape of a silver feeding dish.

Nancy Reagan was so busy with the "towel brigade" at the Reagans' 688-acre California ranch last week that she never did get to her reading material -- including daughter Patti Davis' autobiographical novel, "Home Front."

Elaine Crispen, the first lady's press secretary, said the Reagans had to spend so much time mopping up rainwater that came in the front door of their adobe ranchhouse that "it wasn't much of a vacation."

In the current issue of People magazine, Patti Davis says her mother and the first lady in the novel are similar in that they share a sense of "rigidity" because of what they gave up for their ambitious husbands.

"There is a type of woman -- and my mother is one -- who has given up a lot for her man. The more prominent your husband is, the larger his ambitions are, the more you have to give up. When you do that," Davis told People, "there's a rigidity that comes."

Like Davis, who rebelled against her parents by speaking out against nuclear war and in favor of a woman's right to have an abortion, the book's heroine, Beth Canfield, is at odds with her parents. Beth's father is a well-intentioned if square politician who eventually becomes president; her mother is cold, unbending and concerned about appearances.

The Reagans received their copy of the book a week ago. Davis and coauthor Maureen Strange Foster received a six-figure advance from Crown Publishers Inc.

For four years, political humor writer Alan De Valerio was "At Your Service, Mr. President," working as a White House butler privy to gaffes, goofs and gossip.

Then one night about a year ago, after the Reagans' dinner for the queen of Thailand, De Valerio bumped into the president, who was on his way to bed.

"I always used to keep a copy of some of my one-line jokes in my pocket, and since there was no one around, I asked the president if he would be interested in reading some of them," De Valerio writes in the March issue of Tables magazine.

Never one to pass up a one-liner, the president not only read De Valerio's jokes but laughed at them. That it was no laughing matter became clear before the evening was over when then-Chief Usher Rex Scouten, who happened upon the duo, later ordered De Valerio fired. De Valerio says he doubts the president ever knew anything about it.

The domestic staff never speaks to the president unless he speaks first, says De Valerio. While clearly at fault, he says he wondered at first: "Were my jokes really that bad?"