I’ve seen it listed as an error (for example, here at Movie-Mistakes.com) when, in Indiana Jones and the Last Crusade, Hitler autographs Indy’s book using “Adolf” rather than the properly-German “Adolph”. Lend that what credence you may.
John Toland’s bio of Hitler has his birth certificate, which calls him “Adolfus”. It’s apparently issued by a parish priest, so Adolf is correct. FWIW, I’ve pretty well always seen it spelled with an f.
Apparently, he used Adolf throughout his life, and his signature of his first name ended with a line with a crossstroke, presumably forming a f.
We’ve had two kings called Gustav Adolf (and another four called just Gustav/Gustaf), none of them called Gustavus Adoplhus. The older of them, Gustav II Adolf, is called Gustavus Adolphus by foreigners, though. Don’t ask me why (on the other hand we tend to swedisize names of foreign regents, so I assume it’s just fair).
In case you wonder about the numbering of Swedish kings we always put the number after the first name if they have more than one. Thus you get Carl XII, Carl XIV Johan (Jean Baptiste Bernadotte) and Carl XVI Gustaf (also called ‘Cal Gustf’ or ‘knugen’ (ie ‘the knig’ in English) because of his dyslexia).
Just to answer the OP, Hitler’s first name was spelled “Adolf” according to Webster’s. It lists no alternate spelling.
Unless the dictionary is wrong, I’d say the movie mistake listing is in error. I took 3 years of German in high school, and I don’t remember seeing any German words that ended in “ph”. Of course, that was a long time ago.