I agree with Ed O'war. Wehrmacht is probably the best name for them.
The Storm Trooper or Sturmabteilung (SA) actually refers to the "Brown Shirts", the thugs who went around terrorizing the jews during the early period of Nazi Germany.
Here is a glossary of German terms I found at
this web site
A
Abteilung - Battalion or Detachment
Armee - Army
Armeeabteilung - Army Detachment
Armeekorps - Army Corps
Aufklärungs - Reconnisence
Ausbildungs - Training
B
Bataillon - Battalion
E
Ersatz - Replacement
F
Feldersatz - Field Replacement
Festungs - Fortress
G
Gebirgs - Mountain
Grenadier - Infantry
H
Heer - German Army
Heeresgruppe - Army Group
I
Infanterie - Infantry
Infanteriegeschütz - Infantry Gun
J
Jäger - Light Moutain or Rifle
K
Kampfgruppe - Battle Group
Kavallerie - Cavalry
Kossacken - Cossack
Kriegsmarine - German Navy
L
Luftlande - Airlanding
Luftwaffe - German Air Force
M
Motorisiert (mot) - Motorized
N
Nachrichten - Signals
Nachschub - Supply
P
Panzer - Armoured or Tank
Panzerabwehr - Tank Defense
Panzergrenadier - Armoured Infantry
Pionier - Pioneer (Combat Engineer)
R
Reiter - Rider
S
Stamm - Cadre
Stellungs - Static
Sicherheits - Security
Sturm - Assault
Sturmgeschütz - Assault Gun
T
Truppen - Troops
W
Wacht - Guard
Wehrmacht - German Armed Forces
As you can see, the Wehrmacht was the combined German Armed Forces.
Another suggestion would be the Panzertruppen
or
das Heer
or
If you want to stick with stormtrooper why not change it to Sturmtruppen?
I don't think there were any actual units in the Wehrmacht called sturmtruppen but with German they make up words all the time. That's one of the things I loved about studying German. You could just make up words by combining other words endlessly, i.e. Panzervernichtungstrupp (tank destroying troops). Got to love that German, what a sexy language.