That's a very good thing, and it's what you will need to train yourself to do. When I first went back on solid foods, I only put on my plate the amount I was told to eat. When I finished, I wanted more. But that was just my old habits talking. When I asked myself "Are you still hungry" the answer was NO. That was a HUGE realization for me, that my wanting more had nothing to do with my hunger. I still struggle with it to this day, almost 18 months after surgery.
Portion, portion, portion - get to know what a portion size basically looks like, then when you eat away from home you can make better choices about how much to eat. Ask the waiter to go ahead and bring out a to-go box, and box up the rest of your meal before you even start eating. Don't try to rely on feeling "full". If you are like me, and many other overweight people, we don't really know what full feels like. Over-full and uncomfortable was generally our stopping point. That's why I go by portion.
You also said you don't allow yourself to snack, but you get hungry between meals, and you don't want to eat unnecessarily, but only when necessary. If you are truly hungry, then it is necessary to eat. Don't think of them as Snacks, don't eat them for enjoyment - they are fuel.
You are doing fine! The first couple of months are usually the hardest, as you retrain your brain and body, but the struggle will be worth it.