The testimony of Toyota president and CEO Akio Toyoda regarding problems with his company's cars has raised the question of the relationship between his name and that of the company. They are related: he is the grandson of company founder Kiichiro Toyoda. Why then is the family name Toyoda but the company name Toyota? The BBC has done pretty good job on this question, but some further explanation may be useful.
First, a little background. The family name Toyoda is written 豊田 in Chinese characters, とよだ in hiragana, and トヨダ in katakana. The Chinese characters mean "fertile rice paddy". The company name Toyota is written とよた in hiragana and トヨタ in katakana.
Several explanations have been offered for the decision to change the name of the company from Toyoda to Toyota. One is that the change results in an auspicious number of strokes. The difference between the two names when written in kana is the elimination of the two little strokes that form the diacritic that makes /da/ from /ta/. The kana name contains eight strokes, and eight is an auspicious number. (In case you're thinking that トヨタ contains ten strokes, the strokes in question are not lines as you might naively draw them but single brush strokes as they are made in the tradition of Chinese calligraphy. The ㇕ component of /yo/ and the ㇇ component of /ta/ are both written with a single stroke.)
The problems with this explanation are that people don't usually care about the stroke count of words written in kana rather than in Chinese characters, and that the number eight, while auspicious to Chinese people, is not particularly auspicious to Japanese people. Eight does have a traditional cultural association for Japanese people, but it is with large numbers rather than auspiciousness. An example is the name of the Double-Flowered Cherry, 八重桜 yaezakura, a variety with numerous petals, literally "eight-leafed cherry". Of course, it is possible that Risaburo Toyoda was a Sinophile and was more influenced by Chinese numerology than a typical Japanese person might have been.
Another explanation is that Toyota served to dissociate the motor vehicle company from farming, which advanced the company's goal of presenting itself as innovative and high-tech. A third is that voiced sounds like [d] are considered to be "murky" while voiceless sounds like [t] are considered "clear". Finally, it may be that the aesthetics of the logo played a role.
In 1936 the company held a public competition to search for a new logo. The winning entry wrote the name in katakana within a circle, shown schematically below.
To some eyes the version with /d/ (on the left) looks a bit too busy and asymmetric, the version with /t/ (on the right), simpler and more symmetric.
Ironically, in English Toyota and Toyoda tend to be pronounced much the same due to the flapping of intervocalic /t/ and /d/ in casual speech.