Consumer Product Safety Commission Barbara Hackman Franklin yesterday called on President Carter to "name a new chairperson NOW to take over the reins of the commission this summer," but indications are she will not get her wish.

Her Republican colleague on the commission, S. John Byinton, has resigned the chairmanship of the beleagured agency effective June 30.

In a speech before the Society of the Plastic Industry here, Franklin also said she is concerned about rumors that the White House is considering folding the agency and transfering some of its functions to the Environmental Protection Agency and the Department of Health, Education and Welfare.

"The plain truth of the matter is that we have become a target of the president's reorganization drive," she said. "The Carter administration is said to be considering abolishing the commission."

The agency has been the subject of much criticism in recent months, but also has received considerable support from both consumers and industry representatives at Senate hearings held last week to study its reauthorization.

Franklin jumped to the defense of the CPSC, calling assaults on it "so foundation-less and so ferocious that the net result has been to sap the enthusiasm and dediction of our staff."

And, she added, "Careful deliberations were misconstrued (by critics) as regulatory rigor mortis. Adherence to law became bureaucratic bungling. Attempts to merge the best available science with regulation that is intelligent and fair were seen as callousness to the consumer interest."

Franklin cited numerous achievements of the commission in its five-year history, including education campaigns and public warnings. "Over 7 million units of potentially unsafe products have been repaied, replaced or recalled - at little or not cost to consumers," she said.

She said the agency receives 60,000 written inquiries and 76,000 telephone calls a year from consumers. She also counted several product bans and "18 other substantive regulations."

After Democratic commissioners Edith Sloan and Susan King were appointed last month, and R. David Pittle reappointed, the five-person commission was up to full strength for the first time in years. But the uncertainty over who will succeed Byington in June still causes a leadership void that Franklin says must be filled soon "to assure that the transfer of power is systematic and orderly and that the work of the agency does not suffer."

But sources at the White House said yesterday that no successor is expected to be named for "some time."

Pittle has the inside track for the chairmanship, according to the sources but, as Franklin pointed out in her speech, that still would leave a commission opening.

While saying that Pittle's appointment was a likelihood, the administration sources said that they have not even begun to look for another commissioner.

"We have other appointments that are more pressing right now," said a White House personnel office staffer.