Is Grand Duke George a Romanoff or a Hohenzollern?
He is a Romanoff.
Grand Duke George of Russia is the heir to his mother, Grand Duchess Maria of Russia, the Head of the Russian Imperial House. When he worked as an international civil servant of the European Union, he preferred the name George Romanoff, which is his legal name in his Russian passport.
His father, H.R.H. Prince Franz-Wilhelm of Prussia, married his mother in 1976. The marriage followed an inter-dynastic agreement reached between the then Head of the Russian Imperial House, Grand Duke Wladimir, and his brother-in-law, Prince Louis-Ferdinand, Head of the Prussian Royal House. Under the agreement, it was settled that Prinz Franz-Wilhelm would convert to Russian Orthodoxy and receive a Russian grand ducal title prior to the marriage and that children of the marriage would be Russian dynasts, with grand ducal rank and the qualification of Imperial Highness. (In a similar way, the Prince of Wales is a British prince, not a Greek prince, even though his father was Prince Philip of Greece before renouncing his Greek title and being given a British royal title.)
As the son of an equal marriage contracted by Prince Franz-Wilhelm (who never renounced his Prussian title), Grand Duke George, in addition to his primary title as Grand Duke of Russia, also has the right to the title of Prince of Prussia, with the qualification of Royal Highness. (He does not use this title, in the same way that members of other royal houses do not use their secondary titles. For example, the members of the Luxemburg dynasty do not use their secondary title of Prince or Princess of Bourbon-Parma and the members of the Romanian dynasty do not use their secondary title of Prince or Princess of Hohenzollern.)
It should be remembered too that the Russian dynasty has called itself the House of Romanoff from 1613 to today, even though the male line of the House of Romanoff actually died out in 1762, with the death of Empress Elizabeth of Russia, the daughter of Peter the Great. She was succeeded by her nephew, Emperor Peter III. Peter III was born in Germany as Prince Karl Peter Ulrich of Holstein, the son of a German father (Duke Karl-Friedrich of Holstein-Gottorp) and a Russian mother (Grand Duchess Anna, daughter of Peter the Great). His aunt, Empress Elizabeth, who had no children, called him to Russia in 1742 when he was 14 and named him heir to the Russian throne, with the title of Grand Duke of Russia. All of the Russian dynastic heads from Peter III’s son Emperor Paul I to Grand Duchess Maria today technically descend in the direct male line from the German House of Holstein. Despite this, the descendants of Karl Peter Ulrich of Holstein, later Emperor Peter III of Russia, called themselves the House of Romanoff (although some reference books used the name House of Romanoff-Holstein-Gottorp) and did not use their secondary title of Prince or Princess of Holstein. When Grand Duke George succeeds his mother as dynastic head, the Russian dynasty will continue to be called the House of Romanoff.