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How long could an empire last with a name that is hyphenated between two or more identities? Most realms with hyphenated names hurried to choose one identity -- the Bactrians, the Crown of Aragon superseding the Catalan principalities, the Crown of Spain being used to refer to the collection of kingdoms, etc.
This would be the state's "shortest name" rather than the often long, overcomplicated titles of many past monarchs.
Historically or speculatively, what empires are possible with hyphenated names and could there be one that lasts for hundreds or thousands of years? The longest lived seems to be the Holy Roman Empire, also called Holy Roman-Germanic Empire, but it was not a centralized realm for very long.
Some examples:
OTL
Austro-Hungarian Empire
Indo-Greek Kingdom
Greco-Bactrian Kingdom
Holy Roman-Germanic Empire (contemporary name of the Holy Roman Empire)