panzergeist is really cool--Definately sounds Nazi-like.
The thing to remember is that there probably won't be an official name for these things for perhaps even 50 years. The gnomes will call them one thing (probably living armors, or some variation that represents how the experiment has been twisted, such as tainted armors). the Archemaign will call them something else (such as panzergeist). Soldiers in the army that uses them will probably give them some kind of dismissive nickname (such as cogs or clanks), and Soldiers in the opposing army will have some kind of sinsiter nickname (machine terrors, geardevils, armorbeasts, etc) The leaders of the two warring countries will probably have a more formal name for them (automata), or might take the lead of the Archemaign (for the allies), or the remaining gnomes/the party/the soldiers on the battlefield/however they find out (for the enemies).
Finally, at some point, these things are going to come up with a name for themselves, probably something that de-emphasizes both their machinelike state and war-influenced origins, while highlighting the similarities with the non-construct races. For that, I'd suggest the cousins.