Quoting from the 100 Jahre Steyr company centenary publication of 1964, the firm was created in 1864 as Waffenfabrik Josef und Franz Werndl & Comp., in Steyr, Austria.

In 1869 it was coverted into a joint-stock company known as Osterreichische Waffenfabriks-Gesellschaft, (Austrian Arms Manufacture Company). There's an umlaut over the "O".

In 1927 the company name was changed to Steyr-Werke A.G. Among other things they started to make vehicles from 1920 onwards.

The Great Depression hit the firm's bankers hard and the companies assets were acquired by the Kreditstalt Am Hof Bank. This bank also had a controlling interest in Steyr's chief automobile manufacturing compeditor, Austro-Daimler. So in 1934 the Steyr company was joined with Austro-Daimler-Puchwerke. So it then became Steyr-Daimler-Puch A.G.

If you have a look on the recievers of Steyr made firearms, they'll reflect these changes at these time periods.