Prior to 800, it was simply called "The Empire". There was only one Empire in Christendom, so why bother with anything other than "The Empire"? And up to the 12th century, the name "Holy Roman Empire" was never used consistently. Further, it was never clear that for a non-Roman emperor to be associated with Rome was a good thing.

In 800, Charlemagne had been granted the title Imperator Romanorum By Pope Leo III, but he didn't use it lest he offend the real Roman Empire in Byzantium. His later successor Otto III started to use the title consistently, and in 998 adopted the motto Renovatio imperii Romanorum. A convenient political statement perhaps, but he was not much closer in restoring the Roman empire than anybody prior. Over time, however, successive emperors started to use the title more consistently and over time it became the norm.

At the same time, the Popes in Rome happily played along. They wanted a useful-but-distant emperor, lest the emperor meddle in the actual business of ruling Rome.

So between the emperors and Popes came a complex charade wherein the emperors use the prestige of the Holy Roman Empire and papal blessing to strengthen their rule, and the popes keep these emperors at arms' length. Or in most cases, arms long enough to keep them mostly north of the Alps.