Chuck Sambuchino offers his opinion in two phases (emphasis his):
When can you call yourself a writer in private?
Now. Absolutely right now.
Tell yourself in the mirror before you brush your teeth, then again when you’re driving home from work.
Say it so many times that you get exasperated looks from your spouse. Heck, get business cards printed, too. I remember reading somewhere that Robert De Niro will sometimes repeat his lines dozens of times before filming a scene, in an effort to make himself fully believe what he’s saying. That’s your goal: say it, then say it again until you believe it.
When can you call yourself a writer in public?
The answer to this question is also now – but this is a different matter altogether. The reason you want to take this step immediately in public is to apply pressure to yourself. If you start telling people that you’re in the middle of a novel, then you darn well better be in the middle of a novel.