The Reagan administration has figured out a foolproof way to keep its special Puerto Rican task force from being lobbied by Puerto Ricans. The solution is to keep secret the names of the members of the task force, set up with some fanfare six weeks ago to make sure the administration stays mindful of Puerto Rico's problems.

White House deputy press secretary Larry Speakes confirmed yesterday that the administration is withholding the identity of what he called "the secret task force on Puerto Rico" but promised that he would bet the names within a few days.

The administration's refusal to identity the task force members reportedly has irritated the administration of Puerto Rico Gov. Carlos Romero Barcelo, particularly since the body was supposed to funnel Puerto Rican concerns to the White House. But Romero has kept publicly quiet because Puerto Rico, which is harder hit by the Reagan budget cuts than most American states, is heavily dependent on the administration's good will.

Island newspaper, however, have been sharply critical of the administration strategy. The San Juan Star said, "The Reagan administration keeps setting new standards of arrogance in dealing with Puerto Rico," and asked rhetorically: "Would they dare do such a thing with Texas, Missouri, the oil lobby, the milk interests or any of the other countless entities whose interests they deal with?"

The task force was announced April 10 by White House counselor Edwin Meese III while President Reagan was recovering from his gunshot wound. Meese named Richard S. Williamson, assistant to the president for intergovermental affairs, to head it and said that the members would include assistant secretaries from seven Cabinet departments plus representatives from the vice president's office, the Office of Management and Budget and the White House policy development office.

Ever since, Puerto Ricans have been trying to find out who these assistant secretaries are so they can tell them about their problems. The task force was formed with the understanding that Puerto Rico may need special attention because of the impact of the budget cuts, like the reduction in the food stamp program and other programs targeted toward the poor.

Reportedly, the administration acknowledges that Puerto Rico has special problems but is concerned that any action alleviating the plight of the island could set a precedent for other constituencies.

President Reagan spent a varied day at the White House yesterday, meeting with aides and congressional leaders to discuss his pending tax cut proposal before playing host to a seminar for European and South African business executives organized by Time, Inc. The executives pay their own way for the trip and are also briefed by members of Congress.

Reagan met with the group of 38 persons for about 20 minutes in the Blue Room in what aides said was the first program of its kind held by the administration. Similar groups of traveling executives were brought in by Time to meet presidents Nixon and Carter, said a White House press spokesman.

The announcement provoked a brief furor at the daily White House press briefing, with one reporter asking if the president would also welcome his publication's advertisers.

Speakes gave a positive, if jocular, response, saying about Reagan: "He likes everybody."

Earlier, Speakes dismissed a new round of reports that the White House was still looking for a yacht on which Reagan could cruise the Potomac.

The White House did check at one point to see if any Navy boats were available, found nothing that was suitable and dropped the idea, Speakes said.