National Bank of Washington's newly elected president and chief executive, Dale L. Jernberg, said yesterday that he will present a broad program of goals for the bank to a board meeting next month, to inaugurate his stewardship of the city's third-largest and oldest bank.

At the same time, financial community sources said that outgoing chairman and chief executive Donald D. Notman-whose surprise departure was announced late Wednesday, effective Dec. 29-had been asked to resign.

To succeed Notman as chairman, the NBW board picked one of its own members and one of the most visible Washington business leaders over the past wo decades-Giant Food Inc. chairman Joseph B. Danzansky.

But as chief executive and the man who will run the bank, the board selected Jernberg, an NBW official for 23 years-most recently as vice chairman and executive vice president.

Walton W. (Hank) Sanderson, who was president and will now become vice chairman, emphasized yesterday that Jernberg is the new "No. 1 man." Danzansky will not be an active bank manager but, in effect, will expand on his previous role as an NBW director since 1969.

Jernberg was being greeted by well-wishes outside his office yesterday afternoon, on the main bank floor at NBW's downtown headquarters. And he received many telephone calls of congratualtions from outside the bank. too.

In an interview, Jernberg said, "I'm still on cloud nine." But, he hastened to add: "Not that I'm happy about" Notman's departure. "Don Notmman has been a good bankin officer. The bank has prospered.We had our problems when he came and I know we're going to miss him."

According to the business community sources, the board the unhappy with Notman's performance only for one reason-a perceived lack of involvement in the Washington community. "He just didn't go out here . . . he never was close to local situations," one businessman said.

Notman came to NBW from Buffalo, where he had been senior vice president of Marine Medland-Western. He was picked after a six-month search for a man to replace the flamboyant former diplomat True Davis, who was ousted after three years as NBW% chairman.

Along with Wanderson, an outgoing native of the Washington area whose father worked 48 years at NBW, Notman adopted a collegial form of management to replace the one-man rule of the past.

Notman inherited leadership of a bank that suffered greatly from adverse publicity in the late 1960s, when the United Mine Workers Union and the bank were named in a $72 million lawsuit alleging a conspiracy to deprive miners of money rightfully belonging to them. The union owns about three fourths of NBW stockcurrently its biggest single investment.

Under Notman, deposits resumed a growth pattern and profits have never been greater. In terms of technical ability and "one-on-one" dealings with bank customers, Notman was described as among the best in his field.

But bank directors reportedly decided that with the bank now restored to health, it is time to seek a more aggressive identity in the growing Washington market. Notman agreed to step down amicably and will stay as a consultant for one year, after which he may return to New York.

As for Danzansky, in his new role of banker, he is expected to remain as chairman for at least two or three years. He agreed to take the job, and to give up the chairmanship of Giant Food, "at management's request," he said, and Giant president Israel Cohen will now take over as chairman of the food chain in addition to his current chief executive's job. Danzanskyis 63 years old and could remain on the NBW board until a mandatory retirement age of 70.

In an interview, Jernberg described Danzansky's new duties as "essentially those of a director, with long experience in management that will be of great help to us . . . He is a community and civic minded person, which will be helpful and healthy for the bank, for I've felt that this is a necessary part of banking."

With Danzansky providing this broader community involvement that directors found lacking in the former management, Jernberg will run the bank. Doing a little bit of both will be Sanderson as vice chairman, aiding both the chairman and chief executive in their roles.

Danzansky emphasized that he is "very ambivalent" about leaving Giant Food, where he was president and chief executive from 1964 to 1978. "Those were 14 great years . . . I loved every minute of the time."

When other NBW directors approached him with their suggestion that he become chairman, "I told them I wasn't interested in starting a third career," said Danzansky, also a lawyer. But he agreed and reportedly promised to stay at least three years.

Businessmen who are NBW customers welcomed the choice of Jernberg as chief executive. One said he wasn't able to get decisions by going to Notman or Sanderson, but that Jotman "got things done." Another described him as "first class."

Jernberg was employed by Liberty National Bank in 1955, and that bank merged with NBW in 1957. He is first vice president of the D.C. Bankers Association and is scheduled to become president of that group next summer.

He said yesterday that there are "great opportunities" for bankers in the Washington area, particularly in the international business arena where NBW has been increasing its role.

Bamking in Washington for many years was "a sleepy town environment" but has changed dramatically in the 1970s and is becoming more competitive, he said. Also, "there was kind of a club atmosphere" among the bankers and "that day is gone, but there still is a lot of respect by bankers for the other institutions."

Jernberg forecast that smaller banks will find it more difficult as time goes on, "although they can provide more personal service in many instances than larger banks."

Jernberg said savings and loan associations and credit unions will continue to expand their retail or consumer oriented banking services, bring "from the consumers' standpoint, a benefit." But banks always will have larger roles to play in commercial and corporate, as well as international areas, he said.