After a strong first blush of delight in the business world that President Carter had not named some fuzzyminded economist to replace Arthur Burns as the nation's central banker, sober second thoughts about G. William Miller began to form.

Businessmen accept the fact that as chairman of the Federal Reserve Board, business tycoon Miller will be less independent than Burns - indeed, will take part in Carter administration policymaking. What worries them is that this change in role may be matched by a change in policy.

Certainly, the impression conveyed by the White House of Miller as some kind of a younger Arthur Burns is contradicted by the political reasons for the change. Cartee replaced Burns at the risk of further undercutting shaky business confidence throughout the nation and the world in order to satisfy important political constituencies. That makes nonsense out of perpetuating Burnsism-without-Burns at the Fed.

Exhibit No. 1 for the contention that Miller does not spell Burns is an article by Miller in the Oct. 5, 1974, edition of Business Week. Studied by the President's men before Miller's selection, the article proposes wide-ranging government action to induce anti-inflationary conduct by the public. That suggests the faith in governmental problem-solving characteristic of the administration.

One suggestion in particular would chill bankers, businesmen and probably Burns himself: a proposal to classify bank loans by their purpose into "high priority" loans (for example, a mortgage or small-business loan) and less important "low priority" loans. "High priority" loans would rate "a decrease or even a credit" in required bank reserves; "low priority" loans would require "larger bank reserves" and most important - "a mandatory interest surcharge."

To one Wall Street acquaintance, Miller is a "tinkerer." That does not make him a liberal but perhaps a social engineer - philosophically at ease in the Carter White House. If true, he does not meet the business community's desire for a symbol of stability and conservatism at the Fed.

The meaning of Miller can be put in perspective only with this central fact: No serious thought was ever given to reappointing Burns. Not one adviser - not even business-oriented Bert Lance or Robert Strauss - recommended it. The President could not risk the wrath that would bring down on him from labor, blacks and the Senate's liberal bloc led by Sen. Edward M. Kennedy (D-Mass).

In short, the rumored Burns debate, pro and con, was a non-event. The President's economic policy team agreed over breakfast the first week of September that Burns must go. About two months later, Carter approved their recommendation but did not announce it.

The next six to eight weeks befor the decision became public Dec. 28 are explained at the White House as time needed to find an economic look-alike to replace Burns. But competent businessmen and bankers with the Burns mindset come by the limousine-load. What the President sought was somebody was looked like Burns but thought differently.

One requirement was a businessman as attuned to the problems of unemployment as of inflation. Another was a good soldier who would not, as Arthur Burns did, publicly attack the President's proposed $50 tax rebate or write Carter a letter (cetain to leak) attacking his scheme to reduce the capital-gains preference. "We don't want to be hit from the blind-side by the Fed chairman anymore," one aide explained.

The White House now admits that regular presidential meetings with Burns were mostly window dressing. It wants the new chairman of the Fed to become involved in administration policymaking. Thus, the job description: somebody compatible with the Carter team but also acceptable to the business community.

The 1974 Business Week article seemed to satisfy the first requirement for Miller. That he passed the second requirement was shown by the Dec. 28 reaction to his appointment. Approval came from the knights of the Business Round Table, General Electric's Reginald Jones and duPont's Irving Shapiro. Pierre Rinfret, the Republican economic consultant who had urged Burn's retention, called Miller an incredibly good choice. Most important, Burns himself stood by, approvint, as Miller was unveiled to the world (a major objective of Vice President Mondale, chief talent-scout for the job).

Those sober second thoughts set in almost immediately, with several businessmen noting a superficial resemblance between Miller and another progressive-minded corporation president, Treasury Secretary W. Michael Blumenthal. Publicly, few businessmen are complaining about the nation's new central banker; privately, many will urge Arthur Burns not to resign his seat on the board but to keep watch on his successor.