That is false. It was called the “Holy Roman Empire” from the 13th century until 1512. The name was changed in 1512 to “Holy Roman Empire of the German Nation”. But even in many official texts after 1512 they still left out the latter part.
https://en.wikipedia.org/wiki/Holy_Roman_Empire#Name_and_general_perception
There are earlier instances in which rulers of the HRE would refer to themselves as “Holy Roman Emperor and king of the Germans” as separate titles (usually along with a whole bunch more, as was the way of powerful feudal rulers). When they did this usually depended on who the intended audience was. Speaking to the king of France and don’t much like him? Assert your position as heir to the Roman Empire and therefore above him. Trying to get on good terms with the Byzantine emperor, who considers your claim to the Roman Empire to be a usurpation of his own title? Probably call yourself king of the Germans.
