There are many reasons you may feel "hungry".
You might have excess acid production. The acid can causing a "hunger" sensation, and as it moves further up the esophagus, will then lead to true heart burn and pain. If this is the case, using an acid reducer, or proton pump inhibitor (PPI) such as Prilosec (Omeprazole) can be VERY useful. I take a 20 mg Omeprazole tablet 2 x per day and it keeps things nicely under control for me.
As well, the most likely culprit for hunger is "head hunger". This is where your brain is telling you that you want/need/crave something that your stomach and body will not end up agreeing with. And it's usually in much larger quantities that we can handle now that our stomachs are so tiny.
Your brain, and mouth, are used to ingesting much larger quantities (as we did in the past....that's how we got here.......no portion control!). Now, when you put just a few bitefuls of food on your plate, it makes your brain scream "WTF....you can't live on that.....come on, pile it up baby". That leads to overeating our stomach capacity, pain, nausea, etc.
It takes months to learn what your real capacity is. I'm only a 5 weeks out and I've bought too much food nearly every week, and had to throw things out. I was putting too much on my plate (I thought I could handle 4 oz...and barely made it through 2 oz!).
My new favourite weapon is my digital scale. I weigh EVERYTHING and keep my total meal at about 3 oz. Not only does this prevent me from overeating and feeling just horrible afterwards (pain, nausea, etc.), but I can accurately enter everything into my food log (I use MyFitnessPal) and monitor exactly how many grams of Protein, carbs, fat, etc. I am consuming.
Get yourself a scale and starting weighing everything. You'll quickly learn to "eyeball" the right quantities for yourself.
You don't mention how far out you are post-op. In the first few months, your capacity is constantly changing. In the first month, the swelling is still going down (and therefore your capacity is increasing). In the next few months, you're learning what foods you tolerate well and how much, and which give you problems. It's shifting landscape and you have to learn to "roll with the punches" for a while.
It does get easier!