John V. Pollock, executive vice president of National Bank of Washington, has resigned to become president and chief executive officer of National Bank of Commerce effective May 1.

Pollock, 46, was named executive vice president at NBW in 1979. Before that, as senior vice president, he headed NBW's trust department and organized and directed its asset-liability management division.

Banking sources close to Pollock said his surprise decision to leave NBW was influenced by a desire to "run his own shop" as president and chief executive officer. With NBW Chairman Luther H. Hodges Jr. and President James Melson still relatively young men, Pollock, the third-highest official at NBW, had little hope of advancing there.

Pollock agreed that, as president of Bank of Commerce, he would have an opportunity to be more influential in local banking.

"In light of what's likely to happen in interstate banking, we expect to be a strong factor in local banking," Pollock said of Bank of Commerce. He will succeed Michael Sullivan, who resigned recently to become president of a newly chartered Virginia institution, Bank 2000.

Pollock leaves NBW, the District's third-largest commercial bank ($1.3 billion in assets), after 20 years. His appointment as president of Bank of Commerce, "gives us a lot of credibility and prestige," said Jeffrey Cohen, chairman of the holding company, Commerce Bancorp Inc.

As president of the smaller bank, Pollock "has an opportunity to become a principal shareholder," Cohen added. "We're not looking for an employe. We're looking for a partner."

Cohen headed a group of investors who bought control of Bank of Commerce in 1981. There had been persistent rumors in recent weeks that Cohen would sell his controlling interest in Bank of Commerce. Cohen explained, however, that as part of an agreement with directors of the bank, he will "spread my stock around" in sales to directors "in an effort to dispel the impression that this is Jeff's bank."

Although he plans to continue as chairman of the holding company, Cohen recently resigned as chairman of the bank to devote full time, he said, to the development of a commercial and residential project in the District's Shaw neighborhood.

Sullivan had been president at Bank of Commerce for five years. Senior officials at the bank credited him and former senior vice president, Algier B. Dolan, who also resigned, with turning the bank around. "We're excited for Mike," said David Binderman, chairman of Bank of Commerce. "Mike got this job as president of Bank 2000 because of his performance at Bank of Commerce."

Bank of Commerce's assets have increased from $46 million to $70 million in just under four years. It reported first-quarter earnings of $190,000, compared with $60,000 a year ago. Net income last year totaled $575,000, compared with $273,000 at the end of fiscal 1983.