Joan of Arc is merely an Anglicization of her name. Americans suck at the nasal sound in Jeanne.

Because "Leonardo of Vinci" does not roll off the tongue as well. The "-o" of Leonardo does not merge well with the "o-" in "o"f, and the "-f" does not merge well with the "V" in Vinci. Say Leonardo of Vinci aloud, then Leonardo da Vinci. Which is easier?

So no, not quite arbitrary, but the reason for the Anglicization has more to do with pronunciation than it does with history. I know you are looking for a more historical answer, but the question is probably not up to par for this subreddit (no disrespect intended).