If you're referring to that company specifically, yes, their spelling would not have changed, as it is an Eigenname. The actual name was Erste Donaudampfschiffa

If you're referring to that company specifically, yes, their spelling would not have changed, as it is an Eigenname. The actual name was Erste Donaudampfschiffahrtsgesellschaft (Erste = first). However there were probably a bunch of companies operating steam ships on the danube, which can be reasonably called Donauschifffahrtsgesellschaften ;)