Across New York and California, people with Jewish-sounding names have been receiving telephone calls from two interviewers who have identified themselves as Betty and Harry Goodman and asked whom they planned to support for president, according to the head of a Republican-funded Jewish organization.

In many of the conversations, the interviewers said they were representatives of the National Jewish Coalition and congratulated people who said they support President Reagan, urging them to tell their family and friends to vote Republican.

However, the National Jewish Coalition is an arm of the Republican National Committee working to solicit votes for the Reagan-Bush campaign, a small Manhattan weekly newspaper, The Westsider, has discovered, and Betty and Harry Goodman are actually the names used by dozens of part-time workers, most of them black and Hispanic, who were hired for $4 per hour to make the phone calls.

Bruce Soll, who heads the National Jewish Coalition for the Republican National Committee, confirmed the weekly newspaper's story yesterday and said he was shocked to learn that the telephone interviewers had adopted Jewish-sounding names. Soll added that he had ordered the practice stopped "the second we found out about it."

He said he saw nothing wrong with interviewers not telling people that the National Jewish Coalition is an arm of the Republican National Committee since many of the coalition workers are not Republicans. He estimated that the group is about 50 percent Republican, 30 percent Democrat and 20 percent independent.

Soll said a number of state Republican committees also have local chapters of the National Jewish Coalition, which are handling and paying for the telephone operations, including New York, New Jersey, California, Florida, Illinois, Pennsylvania and Massachusetts. In addition, the Greater Washington D.C. Jewish Coalition is run by the Maryland Republican Party, he said. "If anybody asks, they're told to say it's a Republican-based group." -- Jewish Coalition director Neil Levin

The New York and California operations are the only two being run by paid workers, and are each estimated to cost between $100,000 and $200,000, Soll said.

Soll said his goal is to make certain that Reagan does better with Jewish voters than the 37 percent he received in 1980. Aside from measuring Jewish support, Soll said he is also looking for undecided Jewish voters to target for political mailings.

He added that the Republicans are trying to identify Jewish voters by a number of means, including obtaining synagogue membership lists and mailing lists for Jewish-oriented publications. In addition, he said, they are going through voter registration lists looking for "ethnic" names like "Goldstein" or "Schwartz." He said persons with apparently non-Jewish first names are eliminated, as well as anyone whose name ends in Jr. or III, since such practices are rare for Jews.

The operation came to light after a part-time telephone solicitor for The Westsider responded to an ad in The Village Voice, a weekly Manhattan newspaper, seeking persons to conduct telephone interviews. He did not take the job, but told some of his colleagues about it.

Westsider reporter Jan Bartelli -- using the alias Janet Rose -- in an interview, said that she applied for a job and went to work there as one of a number of "Betty Goodmans."

She said there were about 30 other interviewers there when she started work at 5 p.m. Bartelli said she tried to shield the mouthpiece of her telephone as a loud chorus of other Betty and Harry Goodmans introduced themselves simultaneously over the telephones, some of them in heavy Hispanic accents.

Bartelli said the interviewers were told to identify themselves in the New York calls as representatives of a polling company and in the California calls as affiliated with the National Jewish Coalition, which she said carried "the clear implication that it was a national religious organization."

Neil Levin, executive director of the New York Jewish Coalition, said yesterday that the interviewers were "never instructed by us to use pseudonyms."

He added, "If anybody asks, they're told to say it's a Republican-based group. Nobody tried to hide anything."