Zebrakenko bicycles first appeared in the US during the mid-1970s, just past the Bike Boom's peak.
Like many other Japanese bikes of that era, their lugwork and paint were clean, and they came with good, high-value components from the likes of SunTour, Shimano, Sugino and Sakae Ringyo (SR).
Somewhere along the way--I am guessing in the early or mid-1980s, the name was shortened to "Zebra." It was, I reckon, an attempt to evoke the animal's agility, as I don't recall any of their bikes painted with black and white stripes.
Or, perhaps, whoever rebranded the bikes had this in mind: