When the Holy Roman Empire was at its peak, there was a running joke among the nobility of the era. They said that its name was a misnomer: it wasn’t an empire, it wasn’t Roman, and it certainly wasn’t holy.
When the German Roman Empire was at its peak (say, 1180s or so), no one told this stupid joke because “Holy Roman Empire” was first used in the 1600s, after the Empire had become an empty shell (it collapsed about 1250 and was replaced on the European stage by the rising consolidated kingdoms of France and England; the title continued but it became the basis for the Habsburg house dynasty, which itself split into two branches, one in the nation-state of Spain (and the Netherlands), the other in Austria, eventually the Austro-Hungarian empire).
Holy Roman Empire is a modern term. The actual medieval empire was Frankish under Charles the Great then shifted to the eastern, German, portion of what had been Charles’s realm. It was really established as the German Kingdom/Roman Empire by Otto I ca. 950 and lasted to about 1250. It covered German and northern Italy. At the end it also added southern Italy and Sicily briefly. The elected king of the Germans also held the title of Roman Emperor (since Charlemagne).
So the joke is one of those modern anti-medieval snotnosed jibes at a supposed evil medieval past.
You wrote:
“When the Holy Roman Empire was at its peak, there was a running joke among the nobility of the era. They said that its name was a misnomer: it wasn’t an empire, it wasn’t Roman, and it certainly wasn’t holy.”
Actually, the saying is from Voltaire. He invented it in 1756 - about 50 years before the Holy Roman Empire was dissolved.
Voltaire wrote: “Ce corps qui s’appelait et qui s’appelle encore le saint empire romain n’était en aucune manière ni saint, ni romain, ni empire.”
Translation: “This agglomeration which was called and which still calls itself the Holy Roman Empire was neither holy, nor Roman, nor an empire.”