Enter McGovern -- Democrat No. 7 in presidential race

George McGovern for president. The name and the face rekindle a hundred vivid memories. The Vietnam war. Student protests. Richard Nixon. The Watergate break-in. Democratic Party reforms. Blacks, women, and youth controlling the Democratic convention. The Eagleton affair. Finally, one of the most crushing election defeats in United States history.

Mr. McGovern - ex-senator, ex-Democratic presidential nominee, lately college professor and lecturer - Tuesday became the seventh Democrat to enter the 1984 race for the White House.

He begins late, very late. The liberal wing of the party, where McGovern stands, has already been well staked out.

Walter Mondale, the front-runner, has locked up much of the party's liberal money, talent, and organization, including Big Labor.

Alan Cranston, another liberal, has laid claim to the nuclear freeze movement , where McGovern might have found a natural following. And Gary Hart, who directed McGovern's 1972 campaign, also is working the liberal bastions.

Nor is that the only bit of discouragement. Even McGovern's wife of 39 years, Eleanor, was cool to the race and told him that she won't campaign this time.

Yet McGovern took the plunge. ''You have to do what you have to do,'' he told a friendly crowd of several hundred students here at George Washington University, where he made his formal announcement. ''I'm increasingly uncomfortable on the sidelines. . . . I'm in this race to dramatize my differences with the Reagan administration.''

The 1984 Democratic contest, already an unpredictable scramble, becomes even less certain with McGovern's foray, several analysts say.

First, it could further split the liberal vote. Four of the seven Democratic candidates now espouse liberal causes, and the high-flying Mondale could see his lead, which depends on solid liberal support, erode away.

McGovern's entry could also benefit John Glenn, a moderate, by fragmenting Glenn's liberal opposition.

McGovern's aides say he will run a different kind of race this time - a race at his own, measured pace, a thoughtful race, a race in which he will carefully define and explain the issues.

McGovern's opening-day speech here reflected his new approach. He laid out the broad outlines of his policies; and he was cautious in his criticism of President Reagan.

He argued that Reagan's economic policies have failed. But at the same time he noted that ''the economy was in trouble before the present administration came into power.''

He criticized both Reagan's and other Democrats' calls for higher defense spending. But then he added that US military spending should be reduced only ''after ratifying a verifiable arms control agreement with the Soviet Union.''

McGovern said his campaign would be based on three major propositions:

1. ''There is no longer any alternative to what President Eisenhower described as 'peaceful coexistence' except no existence.'' With enough determination in the White House, he argued that negotiations with the Soviets can succeed.

2. ''The age of big-power intervention in the internal affairs of small countries is over. It does not work any more.'' He added: ''To be specific, as president, I would . . . end all United States military involvement in Central America.''

3. ''American prosperity and power rest on faithfulness to our founding ideals including equal rights and equal opportunities for all Americans.''

McGovern concedes that he worries about ''ridicule'' after his terrible loss in 1972. And so far his plans have been greeted by very few cheers.

The Washington Post growled that in 1972, McGovern took ''commonly held ideas ,'' like opposition to the Vietnam war, and carried them ''to extreme lengths'' that were ''an invitation to isolationism.''

An analyst here close to the liberal camp said: ''Anyone who has lost that badly is discredited forever. Barry Goldwater knew that. Why doesn't McGovern?''

McGovern is hoping the voters won't agree.