Contra most of the other answers here, I don't think it's possible to say that you're definitely eating too few calories and need to ensure you're intaking as many calories as your daily needs if you've got a BMI of over 30. Presumably a good number of calories are coming from stored energy, so that even if you're only consuming 850-1100 calories, a substantially higher number are coming from released body fat, as is natural if you're eating healthily.
So long as you're eating whatever amount it is that you're eating because that's all you feel like physically eating, then there's no reason to think that you're anorexic. From the average daily intake of food described it doesn't sound like you were eating 850 anyway, but if you were, presumably this would be unsustainable. The key is surely is eating until you're full, with little cause for deviating beyond this. So long as you're going to be eating so few calories, then the most important thing is making sure you can meet your requirements within those calories. On paper 80g of protein should be fine, though bear in mind that while you're losing weight your body will tend to consume it's own resources, and so you may need a slightly higher protein intake than you would normally.
N.B. If you're a past anorexic, then you might well want to be very sceptical of the idea that you naturally only want to eat a very small amount of food, but there's no reason why eating a small amount of food per se will give you anorexia. Naturally, if you're aiming to lose weight it might well be very tempting and easy to try to convince yourself that you don't want to eat, but so long as you're constantly vigilant that you're not doing that, there's no intrinsic reason why you should eat more for the sake of it. There is some argument that if you maintain a large caloric deficit over the long term then your body will compensate by 'lowering metabolism,' but if this is a perfectly voluntary result of raised body fat raising leptin, then intuitively, one might not expect this to occur.