The company's name was, I believe, Kōfū something-or-other. Actually it was instead written in Sino-Japanese characters, but Bikeforums' spam prevention or whatever doesn't let me use these. The characters for Kō and fū were/are this and this respectively, so one might english the name as "Bright Wind" or similar. It has only recently become relatively easy to type letters complete with macrons, so it's not at all surprising to see Kōfū rendered as "Kofu".

I know that Kōfū put out bikes branded "Kenkō" or perhaps "Kenko". ("Put out" is deliberately vague. Offhand, I don't know if Kōfū manufactured them or just marketed them.) Kenkō is a very common Japanese word, the standard word for "health" (thus the standard term for health insurance is kenkō hoken).

I don't know of any relationship between the company Kōfū and the city Kōfu, and have no reason to think that there ever was any. (Note that the pronunciations are different, and the ways they are written in Sino-Japanese script are entirely different.)

Kōfū, the company, lives on. Formally, it's Kōfū Ringyō Shōkai. (Ringyō means bicycle business. [It more commonly means forestry business, but that's with different characters.] Shōkai means [commercial] firm.) The company runs both a motorbike shop under its own name (its website) and, not next door but a short way along the same road (Nakahara kaidō), a bicycle shop named Cycland Koowho (its website). ("Koowho" is a rather fanciful way to write what's conventionally written as Kōfū.)

Japanese company websites typically have material about past glories, but neither of Kōfū Ringyō Shōkai's websites bothers with this. The closest I've found is the photo at the top of this page, showing the bike shop as it was in 1960.

The bike shop's website says "Copyright (C) KOOWHO Inc." I don't know what status "Koowho Inc." has, if any; and suspect that it's merely a nonce translation back from Kōfū.

Koowho sells (rather attractive) items with Kenkō advertising. See here.

I've never had reason to enter the motorbike shop. As for Koowho, it's a good, general-purpose bike shop, with a specialty in Moulton (Alex, not Dave). When you're inside, if you look upwards, you see a small selection of old Kenkō bikes mounted on the walls.