Former Virginia governor Linwood Holton Jr. was wading into another crowd of Virginia politicians in the State Capitol, shaking hands, grasping elbows, tapping forearms, and trying all the while to practice the first rule of politicians everywhere: Remember the first name.

Holton grabbed the hand of one lobbyist and pumped it, stretching out the salutation. "H-E-L-L-O," he said in his best southwest mountain drawl, followed by a murmur, "Jame-Georg-ah-Robert."

Then it was down the hallway again, kissing secretaries. He stopped to talk with state Sen. Robert Scott, a Newport News Democrat. "Let me know if I can help you," Holton whispered.

It's been 11 years since Holton was Virginia governor, and he hasn't lost his zest for politicking and persuasion.

Holton, 61, who fought and lost a lot of battles as the state's first Republican governor in 100 years, is walking the marbled halls here and in Washington on what may be his toughest assignment.

Transportation Secretary Elizabeth H. Dole has asked him to clear the way for a plan to transfer ownership of National and Dulles International airports from the federal government to a regional airport authority.

A number of presidents have tried since 1949 to get the federal government to divest itself of one or another of the airports, the only commercial ones owned by the government. Opposition from the airlines, which make money at the airports, and from members of Congress, who enjoy the convenience of National and perquisites such as free parking, have blocked every attempt.

When Dole announced her proposal in June, many in the aviation industry said Holton had no chance of getting the plan approved. But admirers of Holton, who largely has been out of public view since leaving the governor's office in 1974, now say it doesn't pay to bet against the native of Big Stone Gap, Va.

"Holton's personality and intuitive understanding of the issues has done stuff an army of staffers couldn't have done" in promoting the transfer, says a top Transportation official. "He's put together a deal that wouldn't have been possible without him."

The governor has had to summon all his political skills in the effort. "I love the give and take of politics," he says. "I think I'm good at it."

As chairman of a 15-member commission named by Dole, Holton spent six months pleading with warring factions from Virginia, Maryland, the District and the airline industry to agree on recommendations for an airport authority -- and succeeded despite almost universal skepticism.

Holton has devised a strategy to win approval of the plan by first getting the Virginia General Assembly and then the D.C. City Council to endorse the concept. After they act, Holton will ask Congress to pass it.

Disagreements on his commission were so sharp that Holton was barely able to persuade a majority to agree on recommendations in December. In the end, Holton said he swung the deal by convincing D.C. Mayor Marion Barry that Dulles was going to be a booming enterprise, and that the District ought to have a say in running it. "I told him: 'It's going to get away from you,' " Holton said. "And he bought it."

Though his plan barely squeaked through its first round, insiders in Congress and the aviation industry say that Holton has a chance to get the deal through Congress. "Momentum is building," he says. "We have a package that is simply irresistible."

The plan faces objections from a number of quarters, the latest from a group that originally had been the strongest supporters of Holton's effort -- the National Airport antinoise activists.

Noise protesters such as Fred Wood of Arlington, copresident of Washington Airports Council, a group that lobbies to reduce air traffic at National, say they will oppose the plan because the Reagan administration is willing to remove the so-called "cap" of 16 million passengers at National as part of the transfer. That would result in more flights and congestion there, Wood complains.

Airline executives and some congressional sources who decline to be identified said removing the ceiling is the bare minimum their constituencies will demand to support the transfer. DOT officials said the "cap" had to be removed because they could not impose such a rule on a regional authority that had not approved it.

Holton said he will try to win antinoise activists to the plan by telling them, "Everybody's going to have to take some risk and make some compromise."

The passenger "cap" uproar is only the latest in a long line of issues that Holton has been called on to mediate.

Holton was born in southwestern Virginia's historically poor coal field area, which has a tradition of progressive Republicans and few of the racial issues found elsewhere in the state. Educated at Harvard, Holton set up a law practice in Roanoke, and set out to remake the state's moribund Republican Party.

"He single-handedly put together the GOP in Virginia," said Staige D. Blackford Jr., his press spokesman as governor.

Holton shocked conservatives by announcing in his inauguration speech that he wanted to make Virginia "a model in race relations." In the next four years, he raised the number of black state government employes by 25 percent. During his term, Virginia became the first state in the Confederacy to enact open housing laws.

Holton also insulted many Republicans by naming Democrats to some top state jobs. Con- servative Republicans never forgave him. In 1972, in the middle of his term as governor, his party did something unheard of when it voted down his choice for GOP chairman.

Many Virginia politicians still smolder when his name comes up. In recent interviews, old political enemies said Holton is rude, vain and pushy. One said that racism was not the reason so many Virginia politicians bridled at him, but it was "the busing thing," a reference to Holton's decision to accompany his children to Richmond public schools on the first day of integration there.

Holton said he knows that some politicians still dislike him, but that he has felt little hostility on his recent trips from his McLean home to Richmond. He said he is proud of his record as a racial moderate. "If it hurts me, I can't help it," Holton said. "I know it fixes my place in Virginia history, and I'm proud of it."

Stripped of most of his political patronage, Holton left office in 1974 a sort of melancholy figure -- "kind of a forgotten man," said one friend.

He then held a variety of jobs in Washington and each time became restless, friends said. First, he became assistant secretary of state for congressional relations under Henry Kissinger in the middle of Watergate, and quit a year later. In 1978 he ran unsuccessfully for the GOP nomination for the U.S. Senate -- his last attempt at elected office.

Then he took a job as an executive for the American Council of Life Insurance, where he was working last June when Dole asked him to put together the airport plan. Friends said Holton relished the idea of the political maneuvering, and he jumped at it.

Holton's friends say it also cannot hurt a Washington lobbyist to undertake a year-long favor for the transportation secretary. "Mrs. Dole wants this to happen very, very badly," said a top airline industry executive.

Holton, who now works for a Washington law firm, says transferring the airports makes good sense because Washington area residents will have more leverage to reduce airport noise. In addition, he said that given Congress' distaste for spending money nowadays, an authority with power to float tax-free bonds is the only way to raise the approximately $175 million for needed new construction at the two airports.

Holton has found a receptive audience for these views in the General Assembly in Richmond. One reason might be his frequent telephone calls and visits with old friends in the Capitol. House and Senate committees quickly approved bills last week to set up the authority, and little opposition is expected on the floor. In fact, one Senate committee last Tuesday rose in prolonged applause when Holton approached the lectern to speak.

The idea is not expected to be greeted the same way in Congress. Holton fears that Maryland members of Congress, angry because his commission said their state should have only two representatives on the planned 11-member authority, could stop the measure. The other reason Maryland officials may oppose an airport authority is their belief that it would promote Dulles at the expense of Baltimore-Washington International Airport, owned by Maryland.

Holton says this is just the kind of political tight spot he enjoys. In an interview last week, Holton recalled the firestorm he encountered in 1970 when, as governor, he sent his four children to largely black public schools in Richmond under a court-ordered busing plan.

"If it's too easy, it's no fun," said Holton, nodding toward a famous photograph on his office wall of himself escorting daughter Tayloe to a high school that was 96 percent black. "I've done some other things that a lot of people said I couldn't do."