From 1640 to 1918, every ruler of Prussia was named Frederick or William or Frederick William. Frederick William was the Duke of Prussia from 1640 to 1688. He was succeeded by Duke Frederick III of Prussia in 1688, who became King of Prussia in 1701. Then in 1713 came King Frederick William I; in 1740 Frederick II, the famous gay "Frederick the Great," renowned general, respected composer, patron of Voltaire; in 1786 Frederick William II; in 1797 Frederick William III; in 1840 Frederick William IV; in 1861 William I, who remained King of Prussia even after becoming Emperor (Kaiser) William (Wilhelm) I of Germany in 1871; in 1888 Frederick III of Prussia and I of Germany; and later in 1888 William I of Prussia and Germany, the last monarch of Prussia (so far, ha ha), who abdicated in 1918.
Maybe it's just me but it seems strange that for 278 years they couldn't think of any names besides Frederick, William and Frederick William. Albert, George, John, Louis and a few others could've been chosen even without picking a name no ruler of Prussia or Brandenburg had ever had before.
At last, some of the pretenders to the Prussian and German thrones have had different names. for example, Louis Ferdinand, 1907-94, pretender from 1951 to his death. He seems to have been an alright guy. He was an opponent of the Nazis and didn't leave Germany while they were in charge, a gutsy combination even with the mighty protection of his lineage. He was imprisoned after the 20.July 1944 plot, although apparently he had not been involved in it. And it is said that he was a patron of the arts and had some other cool qualities, so there we have it. Also, the medals he had probably could not all have been carried at once by a horse, let alone a man. You want to get a lot of medals? Be born into royalty or a formerly royal family, that seems to be the easiest way.
I'm just sayin' s'all.