The company is Toyota, but the family name of the founder is Toyoda. Why the difference? Bill Poser discusses it at the Log; after citing an implausible theory about stroke count, he says:
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.
He shows alternate versions of the logo, and I have to agree that the one without the dakuten looks better, which is not to say that I believe that version. A useful comment by Gene Buckley says:
An important fact is discussed in the linked BBC article, and is implied by the link to rendaku on Wikipedia by Dan, but it might be useful to make it explicit on this page. The written form 豊田 can be read Toyo-da, with voicing of the initial consonant in the second morpheme, or as Toyo-ta, without this voicing. (Other family names have similar alternate forms, such as 山崎 as Yama-saki and Yama-zaki.) In fact, the pronunciation Toyota is more common as a family name, according to Japanese, Chinese, and Korean surnames and how to read them (W. Hadamitzky, 1998). It’s hard to imagine that the greater currency of this alternate pronunciation of 豊田 played no role in the choice of the company name. The katakana spelling adopted for the company name removes the ambiguity in the pronunciation of the second Chinese character.
(Please ignore the unseemly squabbling about national flapping in the early comments.)