Furthermore, the label also mentions starting in 1400AD from a family recipe. Is that in any way verifiable?
What is the oldest brand we have today, and does it in any way resemble itself at its conception?
I do love when people ask questions I know something about!
Fermented soy paste was first introduced in Japan in the 6th century. The liquid form (shoyu) is believed to have been invented or at least come into common use in the 16th century with large scale brewing operations following in the late 16th and into the 17th century. It really wasn't until the late 17th century that early shoyu would be recognizable as the soy sauce we love today. This makes a 1400s origin for the recipe somewhat unlikely unless we're being very generous with terms. Two of the families which were commercially brewing shoyu in the 17th century would later form a company which is the predecessor to the modern Kikkoman Corporation. An origin in the 1600s is therefore probable.
As an aside, some modern soy sauce producers switched to production techniques which emulate the output of the brewing process without actually fermenting the product. Kikkoman pride themselves on continuing to brew their sauce, despite the additional costs that incurs.
There are many very old brands, some more rightly "brands" than others. Beretta, for example is nearly 500 years old, and has been in the same business throughout. Even older companies exist though, many that could be classified as brands would be manufactures or brewers/distillers/vintners. Staffelter Hof is a winery that dates back to the 9th century and is still in operation. Kongo Gumi is a Japanese construction company founded in the 6th century.
I'm not aware of any research (other than semi-serious journalism) on the absolute oldest brand still in use, which would require a fair amount of rule setting regardless. What classifies as a brand, exactly? Does it have to be intentional branding or can it just be a name? Does it have to be a popular brand currently? Does simply operating a business under the same name for a long time count?
There are many very old businesses arrived the world, several of them in Japan, but many off them are just hotels or manufacturers and haven't necessarily had a well defined brand for their entire life.