In Japanese, the company's name has always been pronounced and spelled as "Matsuda", the name of the founder. Television ads for Mazda automobiles in the United States use a pronunciation where the initial vowel sound is the 'a' in "father", while Canadian Mazda advertisements pronounce the company's name with the initial "a" sound of the word "has". The initial vowel sounds (in the American and Canadian advertisements) are references to the first and last A sounds in the original Persian pronunciation.

Mazda began as the Toyo Cork Kogyo Co., Ltd, founded in Japan in 1920. Toyo Cork Kogyo renamed itself to Toyo Kogyo Co., Ltd. in 1927. Toyo Kogyo moved from manufacturing machine tools to vehicles, with the introduction of the Mazda-Go in 1931. Toyo Kogyo produced weapons for the Japanese military throughout the Second World War, most notably the series 30 through 35 Type 99 rifle. The company formally adopted the Mazda name in 1984, though every automobile sold from the beginning bore that name. The Mazda R360 was introduced in 1960, followed by the Mazda Carol in 1962.

Beginning in the 1960s, Mazda put a major engineering effort into development of the Wankel rotary engine as a way of differentiating themselves from other Japanese auto companies. Beginning with the limited-production Cosmo Sport of 1967 and continuing to the present day with the RX-8, Mazda has become the sole manufacturer of Wankel-type engines mainly by way of attrition (NSU and Citroën both gave up on the design during the 1970s, and prototype efforts by General Motors never made it to production).

This effort to bring attention to themselves apparently helped, as Mazda rapidly began to export its vehicles. Both piston-powered and rotary-powered models made their way around the world, but the rotary models quickly became popular for their combination of good power and light weight (when compared to piston-engined competitors with similar power, usually carrying a heavy V6 or V8 engine). The R100 and the famed RX series (RX-2, RX-3, and RX-4) led the company's export efforts.