Trodat wasn't originally the company's name, just that of a product. The 'Trodat' plastic date stamp was introduced internationally in the 1940s. The name was the product range: 'Tro' derives from trolitul, the material out of which the stamp was manufactured. 'Dat' simply stands for date stamp.
Trodat was registered as an international brand in 1960. In the late 1960s it was selected as the stamp manufacturer's name after reincorporation. You can find out more about Trodat company history here.
The decision to select Trodat as the company's name was made not least because the name easily pronounced in many languages around the world. With an export rate of 98% and customers in 150 countries, that's more important than ever today.