ONE giant merger after another is shaking the United States banking industry. The latest, between Chemical Banking Corp. and Chase Manhattan Corp., was announced yesterday. The combined institution, to take the Chase name, will be the largest bank in the nation with almost $300 billion in assets. That deal dwarfed two other major mergers also announced yesterday: * Cleveland-based National City Corp. has agreed to buy Integra Financial Corp. in Pittsburgh for $2.1 billion. * In St. Louis, Boatmen's Bancshares Inc. announced plans to buy Fourth Financial Corp., a Wichita, Kan.-based institution, for $1.2 billion. ''We have too many banks,'' says Paul Nadler, a professor of finance at Rutgers Graduate School of Management in Newark, N.J. The US has more than 10,000 commercial banks, plus thousands more thrift institutions, investment banks, and other financial institutions that can do some of the same business activities as banks themselves. ''We will see more mergers,'' says Colleen Pantalone, a finance professor at Northeastern University in Boston. ''It is a natural result of deregulation and an attempt to be competitive internationally.'' ''The financial-services industry is in the midst of the greatest period of consolidation in its history, and we are seizing upon a truly unparalleled opportunity to create a premier global financial-services company,'' stated Walter Shipley, chairman and chief executive officer of Chemical. He will take the same position in the merged bank. The two banks figure the merger will result in a cost savings of $1.5 billion within three years, or about 16 percent of combined 1995 operating expenses. Some 12,000 positions from a combined staff of 75,000 located in 39 states and 51 countries are to be eliminated. ''What am I going to do to get jobs for my students?'' asks Professor Nadler. Bank employment in general has been declining across the nation, partially because of the arrival of automatic-teller machines and computerization in general. Mergers, by eliminating jobs, are ''hard on people,'' adds Nadler. But they ''make sense. This is where banking has to go.'' Mergers, however, may even be helpful to some small banks. ''Giant mergers, such as this one, provide an opportunity for independent banks ... to provide a variety of services to business and individuals who may feel disenfranchised by large banks,'' says Edward Liebenstein, executive vice president of Sterling National Bank and Trust Co., a small independent bank in New York. ''We are not replacing the human side of banking with technology as so many banks are doing.'' Big mergers, says James Burnham, a professor of business at Duquesne University, Pittsburgh, do not ''spell the end of smaller innovative banks. Management of smaller institutions will have to think more aggressively and be more innovative and faster on their feet than in the past.'' Nadler says the Chemical-Chase merger will be ''tremendously useful'' for the shareholders of both banks. Shareowners have already seen large profits as their stock prices jumped yesterday. But he says the merged bank will have to work hard to provide the services that will satisfy its 25 million customers. The three necessary services are correcting errors, providing a quick response to requests for service, and showing care for customers by such indications as knowing their names, he says. Because many big institutions have trouble performing these functions, Nadler expects many new smaller banks to spring up: ''A lot of people are going to leave big banks and go to little banks.'' In Pennsylvania, notes Professor Burnham, small banks have become the most profitable by ''disassociating themselves from the bureaucracies of large entities.'' The Chemical-Chase merger leaves 168 commercial banks with a total of $800 billion in assets in New York State. Only four of the top 10 ''money-center banks'' in New York City have not formed a major affiliation in recent years. The merged bank will have about $40 billion more in assets than the nation's No. 2 bank, Citicorp. The new Chase will be the fourth-biggest capitalized bank in the world, with $20 billion in assets. The world's largest banks are Japanese. The merged bank will have offices in 39 states and 51 countries. Cost of the deal was put at $10 billion, almost twice that of the next largest merger, that between First Union and First Fidelity in June 1995. The third largest merger, according to Keefe, Bruyette and Woods Inc. was between First Chicago Corp. and NBD Bancorp Inc. at $5.3 billion.