Do your fish respond to their name? How far do you think they can see?
I have 3 fish in close proximity to each other but separate tanks. I call their name and tell them how pretty they are. They generally only start getting more excited and wiggly (each time) when I specifically say their name.
It also seems like they can see fairly well if I start feed one that is a good distance away the other fish does his I am excited I am going to get fed dance. This does not occur until I pickup the food container and open the other tank.
I don't know about responding to names, but I imagine it's possible. They can see very far though. Mine get very excited when they see me walk in the room. I would say their tanks are a good 10-12 feet from the main door and a good 5 feet further from the bathroom door, and they can tell that I'm there from that distance.
It is not possible for fish to self-identify. Even if it were, they would not be able to hear their names and distinguish the sounds beneath the water. Fish are not aware of themselves in the way that larger animals, such as cats or dogs, are. Betta fish are no exception. It also makes sense that they would not respond to sounds for identification because they do not communicate in such a way; they did not evolve for such purposes. It is hard enough to hear underwater when the sounds come from within the water itself, let alone through the glass, water, and other sounds.
While bettas can not self identify in the way we think of it (why they flare at their own reflection), I believe what is happening in your case is association with food. I (very gently) tap my fishes glass before I feed them and after a couple weeks of "training", they pop right up to the surface. They would definatly hear you say their names, and now they associate that sound with food.
So most articles I have read say they hear vibrations and they can be heard outside the tank.There isn't always or typically food involved in my interactions with my fish. You could be right that they are associating my voice with food. The reaction does seem to be specific. Penelope for example who is hiding in the back of her tank will come forward when I say her name. She does not come forward if I am saying the fishes name next to her. Now I'd agree that the association is probably not a "personhood" thing but it is interesting. It may take awhile for me to find the time but I will try to film their reactions to my voice.
Fish are ultra sensative to vibrations. Sound waves can cause numerous reactions. An example would be in my other favorite pastime, bass fishing. When the water is dirty, you use noise making lures to attract fish from greater distances.
Fish also have keen optic nerves. Being able to see not only helps them locate food, but also avoid predators.
I never call my fish by their names even though they are named, when I come home from class I just go to the tank and look in and say "Hello feesh!" like an idiot xD and they swim right up to the glass to see me. If I'm wearing my sunglasses they flare at me though, but they usually look at me or dance around, they are so silly. When I feed them if they are not present within a few seconds of my opening the lid I will tap on the glass if they are hiding they'll come to the surface for their food. Idk if they can "hear" very well, or how far they can see. I was sitting by the tank the other day and coughed pretty loud and both fish darted into their caves lol So they definitely heard that. But sound waves are just vibrations, tapping on their tank or talking real loud at the glass will cause minute vibrations they can "hear" pretty sure they recognize my face if not my voice though and they definitely recognize the bright red lid of my Omega One Fish Food container lol But they are an Old World fish adapted for living in murky rice paddy water, i imagine they can see fairly well.
I don't think mine know their names, but they respond to my voice. I can stand in front of their tanks and look at them and they don't get really excited and start doing their 'happy dance' until I start talking to them (in silly baby talk, nonetheless, haha). They will react and come to check out my fiance when he looks at them and talks to them, but they don't dance!
I think they can see well - and, like Crazy Diamond, I honestly think they recognize the food container, because when I pick it up (specifically) they react.
I believe a lot of people think bettas are boring fish that just sit around because that's what they see them doing in stores in those awful cups. They don't know how much personality the little things have. I know it's what I thought for a long time - and that's why I never got one. I'm glad I took the plunge and picked up my first boy!
Mine recognize me entering the room from 12 feet away, sensitive to sounds outside of the tank e.g. sneezing. they definitely recognize the sound of opening the NLS container since the foam insert scrubs against the lid. They'd dance for food, jump for food. I now have to cover the cup when I get them out for inspection or WC since they jump at the sight of my hand and I am wimpy owner.
I do call their names by calling them at the top of the tank to generate a certain sound wave since their names are different. I guess it works, but IDK, it could be my own imagination.