^ german wiki gives a clear answer , the actual name is "Jagdpanzer VI Jagdtiger" as extra info Sd.Kfz.186 so maybe all should get that
https://de.wikipedia.org/wiki/Jagdpanzer_VI_Jagdtiger

"Nibelungenwerk" is factory belonging to Steyr-Daimler-Puch AG, the sole 3rd Reich tank factory using assembly line system
https://de.wikipedia.org/wiki/Nibelungenwerk

we have similar issue with american tanks , they were made by DETROIT ARSENAL factory , which belonged to Chrysler hence all those tanks are listed with Chrysler as maker
https://en.wikipedia.org/wiki/Detroit_Arsenal_(Warren,_Michigan)

Jagtiger was made on two chassis first batches on Porsche chassis the last ones on Henschel chassis , that's the Henschel connection


this are the facts