Obvious occasions to restore HRE, or the title thereof, would be 1814-1815, 1848...1849 and 1866...1871.
In OTL, the Reich founded in 1871 desisted from calling itself HRE.
IMO, there was no way the Allies after 1945 were going to restore HRE - Germany had been a republic for 26 years, and no one was hot on monarchies. The obvious time to restore HRE would be 1918...1919.
Suppose that Germany 1918...1919 had more support for a constitutional monarchy. The Second Reich had 27 constituent states - 23 monarchies, 3 republics and the imperial territory of Elsass-Lotring.
WI Wilhelm II personally and House of Hohenzollern are discredited enough that Prussia is declared a republic on 9th of November as per OTL, and so are a few of the less popular monarchies like Bavaria - but most of the other constituent states back their monarchs. How would the Weimar assembly decide about the overall Head of State position, and the name of the country?
Could they elect some of the more popular rulers, like King of Saxony or King of Württemberg, as a constitutional monarch, and underline the change to a more limited monarchy than old Reich by recycling the name of HRE?