I think you can be called a Whovian if you have only seen the new series and not watched the classics. I started watching with Four and stopped after Five and picked up again with Seven and then not again til Ten. I have slowly worked backwards but have not seen all the Classic serials myself.
I think you can have started with RTD and Nine and watched all the way through and still call yourself a Whovian, absolutely. I think knowing the rich history that comes with the Doctor is better but doesn’t define your viewing now 🙂