LABOR SECRETARY Raymond J. Donovan, even before the Justice Department announced its decision yesterday to name a special prosecutor, asked that an investigation begin at once into the latest allegations against him. That would be a useful service, not only to Mr. Donovan--who has naturally been troubled by the slow trickle of information and innuendo--but also to the public. Over the months since his appointment was announced, Mr. Donovan's name has been mentioned repeatedly in investigations of labor union irregularities, and a full accounting of the various charges and rebuttals is needed.

Mr. Donovan's troubles began with a series of allegations that were aired during protracted hearings held on his nomination. At that time the FBI investigated 18 specific charges that the Schiavone Construction Co.--of which Mr. Donovan was part owner and executive vice president in charge of labor relations and other aspects of management--bought labor peace from local unions and was tied to organized crime. Mr. Donovan vehemently denied all accusations of involvement in or knowledge of any of the alleged incidents. The FBI concluded, after a short but intensive investigation, that it could not corroborate the charges.

Mr. Donovan's name reappeared in May in connection with a grand jury investigation of Teamster extortion rackets and in June in connection with court-approved wiretapping of the New York operations of a Schiavone subcontractor said to be linked to the Mafia. Then, in September, allegations of illegal relations between Schiavone and a New York Laborers union local--first made three years ago -- caught the eye of Thomas Puccio, the head of the Federal Organized Crime Task Force in Brooklyn. These last charges were brought to the attention of the attorney general earlier this month, and, after an investigation by the FBI, it was decided that a special prosecutor should be appointed under the Ethics in Government Act.

President Reagan in his press conference last week noted that the appointment of a special prosecutor carries with it no connotation of guilt. That's true. The president also expressed the view that the labor secretary should stay in his job during the investigation, since Mr. Donovan would still have time to perform his duties. This is a different judgment from that made in the case of National Security Adviser Richard Allen, but the distinction may be justified. For whatever reason, Mr. Donovan has involved himself only lightly in the traditional duties of his office. That's a satisfactory arrangement as long as the president does not feel the need for stronger help in handling the numerous employment policy issues that the country now faces.

There is, however, one parallel between the Allen and Donovan cases. The standard to be applied is not simply whether either man committed crimes. There is surely a higher standard of fitness for high public office. The secretary of labor has large responsibilities for ensuring the integrity of labor organizations and pension funds and for combating labor racketeering. He should be a person demonstrably fit to do that.