Clement Haynsworth is still a familiar name but, outside their native states, the names of Kenneth K. Hall and Dickson Phillips hardly are household words.

In the next few weeks, however, the recent work and background of all three men will come under considerable scrutiny.

They are judges on the 4th U.S. Circuit Court of Appeals and all are crucial to the government if it pursues what is generally considered the most likely avenue for fighting Thursday's reversal of Maryland Gov. Marvin Mandel's conviction on political corruption charges.

By a 2-to-1 vote, a 4th Circuit panel ruled that errors by the trial judge in the Mandel case were so serious that the mail fraud and racketeering convictions against the governor and five codefendants had to be reversed.

Justice Department officials said yesterday it is too early to say how or whether the government will proceed in the Mandel case because they just received the 122-page opinion Friday.

Philip B. Heymann, head of the department's criminal division, said he was not familiar with the Mandel decision. But he noted "when we lose any long, hard-fought case, it is common for us to ask for an en bance (full court) hearing."

Attorneys who have argued before the 4th Circuit said it accepts few petitions for rehearing by all seven judges, however.

Judge Harrison L. Winter of Baltimore has disqualified himself from considering the Mandel case, so any government petition for a rehearing by the full court would require a favorable vote by four of the remaining six judges.

H. Emory Widener Jr. and Donald Stuart Russell were the two judges who voted to overturn the conviction, so Haynsworth, Hall and Phillips all would have to agree with Judge John D. Butzner Jr., Thursday's dissenter, for the government to win any rehearing.

The government also has the option of asking the U.S. Supreme Court to hear an appeal, seeking a retrial, or dropping the charges entirely.

It is not considered likely that the department would go to the Supreme Court first, Justice officials said yesterday, because the Thursday decision attacked errors by the trial judge rather than the statutes upon which the indictments were based. Thus, the constitutional issues usually necessary for a Supreme Court review seem lacking.

A retrial would be painful for either side because it would be the third Mandel trial. "Triple jeopardy" is the way Mandel's attorney, Arnold M. Weiner, described it.

"I don't know where the hell they would go for a judge this time," William G. H undley, lawyer for codefendant W. Dale Hess, said yesterday.

U.S. District Court Judge John H. Pratt of Washintgon presided at Mandel's first trial, after the 4th Circuit Court of Appeals disqualified Judge Herbert F. Murray of Baltimore. The appeals panel removed Murray from the case, following a defense request, because it was expected that a relative of Murray's would testify at the trial.

After the Mandel case ended in a mistrial in December 1976, Chief Justice of the United States Warren E. Burger appointed Judge Robert Love Taylor of Knoxville, Tenn., to preside at the second trial. Taylor, then 77 years old, had presided at the trial of the late Ohio governor Otto Kerner. Kerner was convicted of conspiracy, bribery, fraud and tax evasion.

The first airing of the charges against Mandel and his associates ended with a mistrial in December 1976 after a jury tampering attempt.

The second trial ended with the conviction in August of 1977.

Russell T. Baker Jr., U. S. attorney for Maryland, and Barnet D. Skolnik, the two federal prosecutors handling the Mandel case, refused to discuss which of the options they are pursuing.

It is general practice, though, for at torneys to study the makeup of any potential appeals panel and to include this information in their decisionmaking equation.

Attorneys who have argued before the 4th Circuit say it is one of the most conservative in the country. All three judges on the original appeals panel are often considered to be proprosecution, according to lawyers who have studied past opinions.

"Widener and Russell went against their usual intentions in this case," one Justice Department attorney familiar with the workings of the 4th Circuit said yesterday.

Prosecutors now must try to weigh whether Russell's background as governor of South Carolina had any effect at all on his pro-Mandel ruling. They also must search for signs that may have persuaded Widener in Mandel's favor, but may not carry over to Haynsworth, Hall and Phillips.

Attorneys familiar with 4th Circuit judges noted yesterday that Widener had raised a strong dissent recently in another case on the same "hearsay" issue that he paid so much attention to in his majority opinion Thursday. In that case, the lawyers said, the judge expressed great concern that admitting hearsay evidence harmed defendants' Sixth Amendment constitutional right to confront witnesses against them.

Haynsworth, the 4th Circuit's chief judge, is best known for the controversy surrounding President Nixon's unsuccessful attempt to put him on the Supreme Court in 1969. Sen. Birch Bayh (D-Ind.) led the Senate fight against the nomination of the conservative circuit judge.

Hall was appointed to the appellate bench by President Ford in 1976. He is a native of West Virginia whose opinions have generated little news in the Washington area.

Phillips is the newest member of the 4th Circuit bench, having been named by President Carter last summer. He is a former dean of the University of North Carolina Law School. Little is known of his court record because he has taken part in so few cases.

Any Justice Department decision to ask the full appeals court for a rehearing must be made by Jan. 25.