Wikipedia says the difference between the spelling in Toyoda's name and Toyota is deliberate - that there were aesthetic and connotative reasons for spelling the company different from the family name. Although obviously, I'm not sure how the exact Japanese writing would work for that.

> But Risaburō Toyoda, who had married into the family and was not born with that name, preferred "Toyota" (トヨタ) because it took eight brush strokes (a lucky number) to write in Japanese, was visually simpler (leaving off the diacritic at the end) and with a voiceless consonant instead of a voiced one (voiced consonants are considered to have a "murky" or "muddy" sound compared to voiceless consonants, which are "clear").

http://en.wikipedia.org/wiki/Toyota

Obviously, though, I don't speak Japanese. Would both the family name and the company name be Latinized as Toyoda?

Same as Honda which is also named after its founder. The transliteration in Honda is modern though, as both Toyota and Honda in Japanese end with a 田.

But back to the naming thing, I think it is not the worst idea to name things after japanese terms, because often they can be pronounced quite easily and are often rather memorable. I have often forgotten company names because they sounded so stupid and hard to remember.