There were several Roman Empires as I recall. The Holy Roman Empire started after the other ones fizzled out.
I had a history teacher who liked to say that the Holy Roman Empire, was neither ‘holy’, ‘Roman’, nor an ‘empire’
For most of its history, it was a loose configuration of Germanic states, that spent more time on internal power struggles than actual governing.
Famously it was neither Holy, nor Roman, nor an Empire.