The brand name sounds vaguely English, the celebrity athlete promoting it is Hispanic and the advertising theme is strictly Madison Avenue, but the product trying to penetrate the U.S. market is Japanese: Bridgestone Tires.

Bridgestone, Japan's dominant producer, is a giant of the worldwide tire industry, fourth in total sales last year behind Michelin of France, Goodyear and Firestone. But 14 years after it first introduced its tires in the United States, Bridgestone has less than 1 percent of the American market. The company is out to change that.

Bridgestone has been running a nationwide advertising campaign -- developed by Dancer Fitzgerald Sample, the same agency that has the Toyota account -- featuring television commercials with golfer Lee Trevino and radio spots using the slogan, "You can feel it when you drive." "It" is the company's "Superfiller" radial tire, which it bills as a "revolutionary" advance in tire technology, promising greater strength at the rim and an improved ride.

Bridgestone is trying to expand its dealer network, offering discounts for bulk orders and picking up 80 percent of shared advertising costs, and has opened new warehouses in Atlanta and Cranbury, N.J. The company is negotiating with Firestone for the purchase of a truck tire plant in Nashville, not far from a new Datsun truck factory.

The objective, according to company officials, is to take Bridgestone's market share up to 3 percent in the next two to three years. The company's U.S. sales were $200 million in 1980. According to Kunio Satake, president of Bridgestone's U.S. division, "We're within target of achieving $300 million in sales. Once we achieve $300 million, we will shoot for $500 million and then $1 billion in sales."

Since the overall tire market is not growing, any gains by Bridgestone will probably be made at the expense of American tire manufacturers, a prospect they do not regard appreciatively. "Bridgestone is very much a real threat," said John J. Nevin, president of Firestone Tire and Rubber Co. "They are a well-managed, very competent company." But, Nevin said, "they don't walk on water." Lacking a U.S. manufacturing plant and the chain of company-owned retail outlets commanded by the major U.S. manufacturers, Bridgestone may not have an easy time improving its market position, he said.

Arvid Jouppi, a respected analyst of the automotive and tire industries, said he doubted that Bridgestone could match Michelin's gains in the U.S. market, gains achieved only at enormous capital cost for constructing new plants financed at prime interest rates. "Bridgestone is a threat, but they are not another Michelin by any means," he said.

A report on Bridgestone by the research staff of Merrill Lynch International in June said Bridgestone and Michelin are the only tire companies in the world experiencing real growth in "a mature and even shrinking industry." Bridgestone, the report said, is characterized by "a strong balance sheet, an excellent product and a favorable product mix," and is likely to move ahead of Firestone into third place in world sales by 1985.

Bridgestone's success has been built on its sophisticated line of truck and off-road tires, which constitute about 70 percent of its export sales, and on the rapid growth of the Japanese automobile industry, for which it is the primary supplier of tires for new cars. In addition, its plants in Japan and its work force are said to be the most productive in the industry. According to the Merrill Lynch report, Bridgestone had $88,000 in sales per employe in 1979, compared to $71,000 for General Tire, the U.S. leader, and $52,000 for Michelin.

The Merrill Lynch report noted that Bridgestone has achieved its $2.25 billion in worldwide sales and 7.5 percent share of the world market even though some of its manufacturing capacity is still tied up in bias-ply tires and the company has not made much of a dent in the U.S. market.

Improving its U.S. position is a key to the company's overall expansion. The first step has been the campaign to increase Bridgestone's brand-name recognition among the consumers who are the target of its growth campaign -- U.S. buyers of replacement tires for automobiles. Reports in the trade press say Bridgestone is spending more than $10 million this year on U.S. advertising, and the company is putting its name forward through sponsorship of events such as the Glen Campbell Los Angeles Open golf tournament and the Long Beach Grand Prix auto race. In the Washington area, Bridgestone has been advertising heavily on radio broadcasts of Baltimore Orioles baseball games.

Some labor officials in the Los Angeles area have charged that Bridgestone's name represents a deliberate attempt to obscure the company's Japanese origins, but company officials scoff at that since they have been using the name for 50 years and are known by it in 150 countries.

The company's founder, Shojiro Ishibashi, created the name by translating his own into English -- stone bridge -- and inverting it, company officials say. Members of the Ishibashi family still control the corporation.

Unlike Michelin, Bridgestone apparently does not plan to construct a U.S. plant for automobile tires. The company has developed a nationwide network of warehouses for storing and distributing tires built in Japan, and its only known plans for a U.S. plant involve the Firestone unit in Nashville that makes radial truck tires.

Because of the plant's proximity to the Smyrna, Tenn., factory where Nissan expects to be turning out 120,000 light Datsun trucks a year by 1983, industry sources assume Bridgestone is aiming to be the original-equipment supplier of tires for those vehicles. Bridgestone executives have toured the plant and have studied economic data on it provided by Firestone. They are expected to announce a decision by the end of the year. CAPTION: Picture 1, Firestone has reached the point where it appears assured of surviving the shakeout analysts say is coming in the stagnant world tire market. By Harry Naltchayan -- The Washington Post; Picture 2, Japan's Bridgestone tire, No. 4 in total world sales, has less than 1 percentr of the U.S. market. The company is out to change that. By Harry Naltchayan -- The Washington Post; Picture 3, KUNIO SATAKE...nearing $300 million sales target