Ironically "Prussia" is where the whole thing breaks down the worst anyway, keeping the old name was worse.

The Old Prussians were eventually entirely culturally genocided by the northern crusades and later Germanization campaigns, but the Hohenzollerns always kept the name going because it being an extra-imperial territory meant they could declare themselves kings in it (then later, of it) and attached the name to a settler aristocracy with no connection to the Prussian people or language.