According to Wikipedia, ‘The College’s official name, College of St Mary, is the same as that of the older Oriel College; hence, it has been referred to as the “New College of St Mary” and is now almost always called “New College”.’
But it shouldn’t ever be called ‘New’, as it is on page 23 of the Michaelmas 2014 issue of Oxford Today. I can cite no written authority for this, but when I matriculated in 1962 somebody eminent — it may have been Anthony Quinton, or possibly even Sir William Hayter, Warden at the time — was quite categorical about the college’s name.
Pedants of the world, unite! You have nothing to lose but your obsessions.