How many ways can you bow in Japan?

This is so comprehensively wrong I don't even know where to start. The kanji for Toyota (豊田) and Toyoda (豊田) are identical. Bitwise identical, even. (And I count 18 brush strokes, which leads me to think that someone thinks the decision was between トヨタ and トヨダ, which is backwards: the pronunciation does not get decided when you need to disambiguate for writing katakana, it gets decided on naming, and anyone who reads 豊田自動車 as Toyoda Jidousha is reading it wrong and has been for more than eighty years now.)

Toyota Motors sometimes prefers to use the katakana version of its name (トヨタ) in preference to the kanji, but that is basically a branding thing ("it scarcely matters what you pick as long as it is consistent!"). They'll write it with kanji every once in a while too, as will newspapers and the like referring to their country. (This is very roughly similar to newspapers referring to William Jefferson Clinton as "Bill" -- it is an acknowledged correct name other than the canonical one.)

Other companies in the Toyota group standardize on the kanji (such as 豊田自動織機 -- Toyota Industries Corporation) or even on the romaji ("Toyota") versions.

Even though I don't really understand the intricacies, I can usually get-by by overdoing it all the time. When in doubt, bow.