Christoph Dassler, a worker in a German shoe factory in the early twentieth century, had two sons, Adolf and Rudolf. Adolf trained as a cobbler, and the brothers decided to set up a shoe factory of their own - the Gebruder Dassler Schuhfabrik - in their mother's laundry, in their home town of Herzogenaurach. As time went on, a rift grew between the brothers; according to one account because Rudolf was the more enthusiastic Nazi; according to another because of an occasion during an air raid when Adolf and his wife got into his air raid shelter to find Rudolf and his family already there, and Adolf said ‘The dirty bastards are back again’ - referring, he later claimed, to the Allied planes. Rudolf wasn't convinced that’s what he was referring to.
Whatever the reason, in 1948 the partnership broke up for good, and Rudolf moved to new premises on the other side of the river, and set up his own shoe factory, which he originally named Ruda (RUdolf DAssler), but then changed, to Puma.
Meanwhile, Adolf renamed the original company, also after himself. Adolf wasn’t generally known as Adolf, though (especially not by 1948, I imagine) - he was known as Adi. Adi Dassler.
The international headquarters of both companies are still located across the river from one another in the small town of Herzogenaurach. Rudolf and Adolf, who never reconciled, are both buried there too, in the same cemetery... as far away from each another as possible.