MIAMI BEACH, Aug. 8--The Republican National Convention which last night nominated Richard M. Nixon because he was the man who could unify the party, almost split wide open tonight in a floor fight against Nixon's choice for Vice-President, Gov. Spiro T. Agnew of Maryland.

The name of Gov. George Romney of Michigan was placed into nomination by the chairman of the Nevada delegation, amid great cheering from an audience which was noticeably unenthusiastic about Agnew. There was also a move underway to nominate Mayor John V. Lindsay of New York, but the Mayor himself reportedly squelched it. Lindsay, in fact, delivered a seconding speech for Agnew.

While the futile floor fight was waged on national television, blacks fought with Miami police in Liberty City, a Miami slum about six miles away from Miami Beach. Police reported rampant looting. Republican Governor Claude Kirk called in the National Guard and appeared on television at 7 p.m. asking people in the area to spend a quiet night with their families. By midnight, four Blacks were dead and over 75 people were arrested.

In the vice-presidential balloting at Convention Hall, Romney drew 186 votes and 26 other delegates declined to vote for Agnew. Nominating conventions generally accept by unanimous acclamation the choice made by the party's presidential candidate. The small number of votes Romney received was not indicative of the Convention's apparent dissatisfaction with Agnew: the 92-vote New York delegation, for example, voted 84-8 for Agnew because the delegation leaders had been told shortly before in a telephone conversation with Gov. Nelson Rockefeller that Rockefeller felt they should stick with Nixon's choice. Among the eight who decided to vote for Romney anyway was Sen. Jacob K. Javitz. The Massachusetts delegation voted 26 for Agnew, 8 for Romney.

After the balloting. Gov. Romney stood up at his delegation's microphone and asked the Convention to approve Agnew by unanimous acclamation, which it did.

Earlier in the day, Nixon had surprised everyone and irritated many by announcing that Agnew was his choice. The Maryland governor had not been mentioned as a contender by any of the news media. The New York Times this morning devoted the second deck of an eight-column headline to the improving chances of Lindsay. Others considered likely by those who didn't know were Sen. Mark Hatfield (Ore.) and Sen. Charles Percy (III.).

Agnew, who was elected Governor in 1966, has said often that he basically agrees with President Johnson's Vietnam policy. In his acceptance speech last night, he said "Anarchy ,rioting, or even civil disobedience has no constructive purpose in a constitutional republic." In the prepared text, "civil disobedience" was preceded by two words which the governor failed to deliver: "currently stylish."

No one knows for sure why Agnew is Nixon's choice. It was clearly not for anything he will add to the campaign--he is an unknown, and not a dynamic speaker. Agnew did help Nixon's chances for the nomination by giving up his favorite son status and supporting Nixon, but it is not likely that any deal was involved.

Nixon's problem--the one place he did make something of a deal--was that in order to hold Southern votes in line last night against Reagan inroads, he had apparently promised a lot of delegates he would not choose a vice-presidential candidate objectionable to any part of the country. Lindsay and Hatfield were objectionable to the South. Among those acceptable to the South. Agnew had done the most for the Nixon cause.

In Nixon's acceptance speech--a speech which he worked on all last week on Long Island--the GOP's standard-bearer repeatedly attacked the Johnson Administration for its war abroad and its lawlessness at home.

Nixon indirectly attacked the Supreme Court. "Let us recognize," he said, "that some of our courts in their decisions have gone too far in weakening the peace forces as against the criminal forces and we must act to restore that balance."

He drew his biggest standing ovation of the evening when he said, "When respect for the United States has fallen so low that a fourth-rate military power like North Korea will hijack a United States vessel on the high seas, it is time for new leadership to restore respect for the United States of America.