President Reagan turned back to his campaign targets of waste and fraud in government yesterday as he named a new comptroller general and urged his inspectors general to "go get 'em."

The new comptroller general, assuming Senate confirmation, will be Charles A. Bowsher, 50, a native of Elkhart, Ind., who has specialized in federal financial and management problems as the managing general partner of Arthur Andersen & Co. here. The president called him "uniquely qualified" for the job as head of the General Accounting Office, the congressional agency that audits the executive branch.

The appointment, for 15 years, is "one of the most important appointments I shall make," the president said. "The problem of waste and fraud in government is an unrelenting national scandal," he declared. "We will continue to move methodically but vigorously in this area."

"I hope you never lose that sense of indignation every citizen feels over waste and fraud in government," Reagan told Bowsher.

Reagan also met yesterday with Edwin L. Harper, chairman of the President's Council on Integrity and Efficiency and deputy director of the Office of Management and Budget. Harper and several departmental IGs gave the president a report on their first six months, and he told them, "You sure have my backing: go get 'em."

Harper reported that since the first of the year IGs have questioned more than $1 billion in costs, have recovered $95 million and have saved $300 million that would have been spent had they not intervened. He said investigations have resulted in more than 600 indictments and more than 400 convictions.

At a press conference later, Harper said the IGs, all members of the council, are going to work together in the next few months to examine management practices in four major areas:

People understating their incomes to qualify for government-financed benefits, such as food stamps or low-income rent subsidies. Thomas McBride, new IG at Labor, said computer sampling will be used to cross-check the income claims of applicants for various benefits. An early sampling of food-stamp recipients in major southeastern cities, he said, showed that about 30 percent of those reporting earned income understated the amount. "In my view, this has the highest potential dollar impact" in the government's anti-fraud campaign, McBride said.

Change orders, or modifications, on federally funded construction. "We're getting some indication that if construction funds haven't been used by the end of the year, and would have to be turned back, they are being applied to change orders," said Joseph Welsch, IG-designate for the Department of Transportation. He will head the IG team studying change orders on federally funded construction.

Unliquidated obligations. There are more than $400 billion in obligations on the books of various departments, and the suspicion is that not all is really needed. Some federally approved projects will never be started and others that are completed have not been closed out: thus the money stays on the books when it could be used for something else.

Eligibility of small businesses to receive non-competitive government-funded contracts. Some random checks, according to Paul Boucher, IG at the Small Business Administration, have found that many firms do not qualify for the special treatment intended to help minority-owned or socially disadvantaged small firms.