In most cases, someone just went to where they could get something made for the lowest price resulting in the highest markup and profit for themselves. And to many consumers a type of Asian 'quality' will be perceived even if not actually present.
Sometimes the name might be chosen to seem familiar but it's really not, in an attempt to generate perceived quality. An exaggerated example of this can be found in the Simpsons episode where Homer and Marge go to the outlet mall to buy a new TV set. They find 'brand names' such as Magnetbox and Sorny.
In some cases, even a 'name brand' item might be truly a fujinoname if it was made by someone else and just has the name brand label on it for marketing purposes. Tandy/Radio Shack, for example, doesn't really make a lot of products. People who paid attention in the past might have noticed that many items sold in Radio Shack stores were identical to items that could be found in other places bearing names such as Pioneer. I have a small "Emerson" TV in the bedroom that I've also seen marketed under names such as Funai. Same item, different name. (Not that either Emerson or Funai is a big-deal brand name, but that isn't the point.) Sometimes they don't even bother putting the 'brand name' on remote controls for such items because it saves relabeling costs.
Many such items are made in generic factories all over the world and simply labeled with whatever name is being used to put them into Wal-Mart stores or whatever. And even if the factory is actually in Upper Slobovia, the item can still be a 'fujinoname' for our purposes.