What was the origin of the name Holy Roman Empire?

Good question, because according to Voltaire it was neither Holy nor Roman nor an Empire.

I'll start with the easiest. It got to be called an empire because after the partition of Charlemagnes empire, there could still be only one emperor, not three. Eligible for the title were his sons and their successors: the king of Germany, the king of France and the King of Lotharingia. Eventually the kingdom of Lotharingia was divided between the other two, and after a number of elections "won" by the king of Germany, the king of France was not even considered. I don't know if this was ever formalized, tbh. The title of emperor is therefore a continuation of Charlemagnes imperial title. In reality, particularly later on, the "empire" was more of a collection of (nearly) independent principalities, duchies, counties.

The term Roman goes even further back. Both medieval European empires, Byzantium en the Holy Roman Empire, claimed to be the rightful continuation of the Roman Empire. Adding in the name Roman stresses that claim. Iirc, this was legitimized in the coronation of Charlemagne by the pope. Note that this was not just a matter of prestige. Being accepted as the successor to the Roman emperors gave a de jure claim to overlordship over all territories belonging to the Roman Empire, so from England to Armenia. Louis XIV warned his successor on his death bed against the aspirations of the Holy Roman Emperor. This is almost 1000 years later!

Holy stems from the claim to be the protector of the faith (Catholicism), and might have been a rightful claim when first used. However, by the 12th century it became clear in the Investiture Controversy that the Papacy and the Holy Roman Empire were at least as much rivals as they were allies. A few centuries later, a large part of the empire wasn't even catholic anymore. So far for that claim.

As for Voltaire's claim: he was probably on the spot. From the point of view of a French catholic the empire most certainly was not holy (Protestantism was by now the dominant religion in many German states), it was German, not Roman, and not an empire but a loose collection of states.