Rafael, Raffael, Raphael, or Raffaello are all correct spellings, depending on where you are (country)
I don't think that's entirely accurate... All of these are recognized names in their respective countries. But as a general rule, a person's name doesn't change when they travel. Raphael is Raphael no matter where he is; 'Rafael' is still a misspelling even if that's the most common spelling for the place he's visiting.
The exception being, I think in various translated versions, his name really is one of those. So then that's the correct spelling.