The German Wikipedia article of Pepsodent is more enlightening: The name is composed of Pepsin, an enzyme for digestion of proteins, plus dent, for tooth. Like Pepsi cola, the toothpaste contained the enzyme, but as it only works in a acidic environment, i.e. a pH value below 5, which is too low for a toothpaste to be harmless for the teeth, it is useless. Thus in 1936 it was no longer contained.

Irium is a brand name of sodium lauryl sulfate, an organic surfactant that is responsible for creating the foam when brushing our teeth.

The Doramad toothpaste copied the style of the advertising from Pepsodent, not its Ingredients, as Pepsodent didn't contain radioactive Thorium compounds or alike.