I have 8 bettas right now and they all have their own personality. I love coming home to see them. I won't tell you about all of them, just acouple :)
Psych (my avatar pic), a Halfmoon, loves when i walk up to his tank and put my finger up to it. He doesn't flare his gills but he fans out his fins for me and dances around. He comes up to the top of the tank when its time to eat and sticks his mouth outside the water and opens and closes it :) . He was my Valentines present to myself this year. lol I've had him the longest out of everyone I've got so far. He likes his dorsal fin being pet too, i think if bettas could purr he would.
Punkin, who is a Veiltail that's body is orange and his fins are purple and turquoise comes up and fans out his fins but doesn't dance. He'll chase your finger around the tank on the surface of the water and will even jump up out of the water if you just hover your finger above it. I got him at PetCo, when I picked up his cup he stared at me and kinda tilted his head like a puppy so i HAD to take him home lol. He's funny because he hates it when i paint my nails, he puffs up his gills and tries to bite my fingers through the side of the tank.
I just recently got another Halfmoon whom I've named Onyx. He was an accidental find at PetCo. I was looking at the babies that they now sell and saw something black staring at me and I looked up at him and he was showing me how pretty he was with his fins all flared out. So I took him home with me. He's a little guy, still young, but I've put him in a 2.5 BettaBow. I was putting a big rock in his tank after I had him already in (i forgot about it) and he was just swimming near by watching. I have a few others who would either try and attack you or run away and hide, but he was watching and when I pulled my arm out he checked the rock out and bit it a few times. lol. Eventually he gave up and just sat on it. He LOVES playing in the filter outflow, he swims against the current till he reaches the top then lets it push him back down and does it all over again. Psych loves doing this too, I think its so cute. He comes over to see me and we just stare at eachother, lol, he's kinda afraid of my finger so we just stare xD .