Much speculation in the bank regulatory arena has centered on who will succeed William M. Isaac as chairman of the Federal Deposit Insurance Corp. Isaac has told the White House he would like to leave by May or June -- or whenever a qualified successor is found and approved.

But the administration also must find a replacement for Irvine Sprague, whose six-year term on the three-member FDIC board ends in February. Like Isaac, whose term expired last spring, Sprague can continue to serve until a successor is approved by the Senate.

Sprague, a Democrat, was named to the FDIC by President Jimmy Carter in 1979. He was chairman until 1981, when he switched positons with Republican Isaac after President Reagan was sworn in. The third member of the FDIC is C.T. Conover, who serves automatically by virtue of his post as comptroller of the currency.

Conover, who has two years left in his five-year term, has not revealed how long he plans to stay, but he has begun to accept speaking engagements for next fall.

Sprague, however, who has worked closely with Isaac during the most tumultuous period in the FDIC's 51-year history, is ready to quit the agency when Isaac does, sources said. FDIC officials said that Isaac and Sprague have worked well together during their six years on the board, but that both are ready to move on.

The Treasury Department is handling the search for successors to Isaac and Sprague. Among the names that have been proposed by the banking industry are C.C. Hope Jr., vice chairman of First Union Bank in North Carolina; Robert McCormick, chairman of Stillwater National Bank and Trust of Oklahoma and a former president of the Independent Bankers Association of America, and Margaret Egginton, Isaac's deputy. Hope and McCormick are Democrats, while Egginton is an independent.

LEGAL STAFF GROWS . . . The FDIC regulates about 9,000 state-chartered banks, insures deposits of up to $100,000 at all but a handful of the nation's 15,000 banks, and is the "receiver" when a bank is closed by either the state regulator or the Office of the Comptroller of the Currency, which supervises the nearly 4,700 nationally chartered banks.

The FDIC's liquidation staff has grown along with the number of failed banks -- 76 this year alone, a post-Depression record. The FDIC legal staff has expanded, too. According to Isaac, the FDIC now is involved in about 20,000 lawsuits, most of them relating to bank failures. Sometimes the FDIC sues -- usually directors, officers and sometimes accountants of failed banks -- in order to recover funds. In other cases the FDIC is sued, usually by creditors or former customers of the failed institution.

As a result of growing litigation, the legal staff has grown from fewer than 100 a year ago to more than 250 today.

ASSESSMENTS RISE . . . For the first time in eight years, the comptroller's office has proposed a general increase in the fee it charges banks for their examination and supervision. The comptroller's office, which lost $7.5 million in fiscal 1983, imposed a 12 percent surcharge on its assessments this year to prevent a $8.3 million shortfall.

The agency, which said its costs are rising faster than its income from banks, would raise its semiannual assessment starting next month and would link the assessments to inflation to assure that income rises fast enough to cover costs.

Smaller banks will face a stiffer increase than bigger banks will. The agency said that, although it costs more to examine a bigger bank, the costs do not rise at the same rate as a bank's assets. For instance, it does not cost twice as much to examine a $100 million bank as it does a $50 million bank, the agency said.

Under the proposed assessment schedule, the comptroller's office would increase the semiannual charge for a $2 million bank from $1,125 to $1,738 -- a 54 percent increase. A bank with $20 billion in assets would pay $726,638 every six months, up from $689,425 or a 5 percent increase.