Common Usage Names?
Panzerjäger known as »Jagdpanzer 38 Hetzer« official name: Panzerjäger 38 (7.5cm Pak 39 (L/48)) (Sd.Kfz. 138/2).
Hetzer was a name of a design that was never produced when instead the Jagdpanzer 38 was selected for production. The name Hetzer was used infrequently by some field units.
Sturmgeschütz known as »Brummbär« official name: Sturmgeschütz IV für 15cm Sturmhaubitze 43 (Sd.Kfz.166)
Its common name was just 'Sturmpanzer', it was never known as Brummbär by the Germans during the war; this is an Allied Intelligence report invention. Its German nickname was "Stupa".
Sturmgeschütz known as »SturmTiger« official name: Sturmmörserwagen 606/4 mit 38cm Raketenwerfer 61
Its common name was 'Panzersturmmörser' and was only occasionally called TigerMörser, never SturmTiger.
The name JAGDPANZER used to differentiate between fully enclosed armoured tank destroyers and PANZERJÄGER for open topped or weakly armoured tank destroyers was never made during the war. War time German documents refer, collectively, to all SP tank destroyers as PANZERJÄGER.
Panzerjäger known as »Jagdpanzer IV« official name: Panzerjäger IV (7.5cm Pak 39 (L/48)) (Sd.Kfz.162)
From January 1944 also known as Sturmgeschütz neue Art
Panzerjäger known as »Panzer IV/70 (V)« official name: Panzerwagen 604/10 (7.5cm Pak 42 (L/70)) (Sd.Kfz.162) Note: name and number, also series number identical to Panzerjäger IV
From 18 July 1944, officially known as Panzer IV lang (V)
Amongst the troops, to differentiate this Jagdpanzer from the PzKpfw IV (lang), it was called Panzer IV/70 (V)
From November 1944, officially known as Panzer IV/70 (V)
Panzerjäger known as »Panzer IV/70 (A)« official name: Panzerwagen 604/9 (7.5cm Pak 42 (L/70)) Note: No series number
Flakpanzer known as »Wirbelwind« official name: Flakpanzerkampfwagen IV (2cm Flak 38-Vierling) (SdKfz 161/4)
Starting in September 1944, 4 Wirbelwind and 4 Möbelwagen were issued to each Pz Flak Zug of these units: PzRg 3/22/33, PzLehr, SSPzRg 1/2/12, PzBrig 111 113, Führer Begleit Brig, sPzAbt 503/506/509, sSSPzAbt 501/503, PzJgAbt 519/559/560/653/654/655. SSPzAbt 17 also had one section of 4 Wirbelwind.
Flakpanzer known as »Ostwind« official name: Flakpanzerkampfwagen IV (3.7cm Flak 43)
Only one Ostwind was ever experimentally test fired (on 27 July 1944) it was sent for troop trials on the western front in September 1944. Whereabouts unknown. Due to intervention and bombing only seven production Ostwind were completed in March 1945. On 1 April 1945, six Ostwind were reported available for use in Bielefeld. This completely contradicts some sources which state April 40 Ostwind were built.
Tiger II: the "Porsche" turret
Krupp was the sole designer of the turrets for the VK 45.02 (H), VK 45.02 (P) and VK 45.03 chassis. What is known as the Porsche turret was designed and built by Krupp for the Porsche design chassis, which was cancelled. The main difference in design was actually electric drive instead of hydraulic. The Porsche name would appear to be another classic Spielberger mistake which everyone has since copied.
Other points of interest:
The cast gun mantlets found on late model StuG's and other Panzerjäger were never known as Saukopf during the war. Original documents refer to them as Topfblende.
Let's not forget the "Bison." I think I've seen references to the "Brummbär" as the StuPa, in Combat History of 653.
I believe many of the names came from British Intelligence or Post-War.
I suppose as long as you and I understand the vehicle being described, "Bison" sure as heck beats typing out 15cm siG33 auf Pz I Ausf B.