I would rename this day if I could. It isn’t a day “on” writing. I had a boss once who would lecture people who said their papers were “on” some topic or another, saying that “on” is the wrong preposition. It still feels wrong here, somehow. This is a day “about” writing or a day “celebrating” writing. It isn’t a day of writing in the sense that we spend the day writing. A day of writing would be like a day of sightseeing or a day of doing laundry–we’d spend the entire day doing that and mostly nothing else. See the distinction? Am I the only one to make the distinction?
And now I’ll dispense with the “scare quotes” (oops) and refer you to the page for the National Day of [sic] Writing (at least it isn’t spelled “writting” [sic]):