It is also somewhat flawed
Ron is correct in stating that the Parabellum brand name was derived from a latin phrase.
DWM intended to use the 'Parabellum' brand name for marketing their military products. They also used it as their telegraph address for quite a while.
The Maxim machinegun they built under license from Vickers was marketed as the Parabellum Machine gun. The luger as the Parabellum Pistol.
So initially it was a brand name, not a product name. But it gradually shifted from brand name towards product name.
'Parabellum' was only the telegraph name for the Berlin office of DWM. Karlsruhe used a different name ('Patronenfabrik KarlsruheBaden)