With the formation of Erich's new government in exile being established, and its status being legally recognized by the Alfheim Dominion, the galaxy had quickly come up with a nickname for Erich's new empire.
Officially, Erich had named his new Empire: "the Germanic Star-Empire." Which was the exact same name used by the territory which Emrys currently ruled over. The reason for this was because Erich considered himself the lawful successor of the previous ruler, and that Emrys was actually a usurper and pretender.
As for the term which he had coined: "the Empire-In-Exile" this was not specific enough considering the fact that there were many of such governments that existed in Alfheim Space. Because of this, the name "Silber Enclave" was quickly established by those who wished to distinguish between the GSE Proper and the new splinter faction that Erich had created.