I ALWAYS have the same problem, I can NEVER think of a name for my bettas! My first one wasn't a problem because I KNEW when I got a fish that I was going to name it Sushi, but then I got a red fish, and I was like braindead, I couldn't think of a name! Eventually I just named him Sashimi for lack of a better idea. Well, eventually I switched my red fish for my friend's purple one, who we named Bitchfish. Its a long story as to that name, but it took us like a month to figure out a name for him! Finally, I couldn't figure out the name for my most recent fish, so I sent a picture of him to my friend and she was like "THATS THE GAYEST FISH EVER!" (because he's pink). Soooo.... he's not supposed to be pink, he's supposed to be all white, but the lighting makes him look pink, so he's 'putting on the red light', so we named him Roxanne. (REALLY corny joke, but still).
So anyway, your fish is beautiful, I'm just warning you to keep an eye on his tail because of the black ends. I got a betta with black on the end of his tail and it looked like his coloring, but it turned out to be fin rot. So just watch him and keep the water clean etc. just because I wouldn't want your poor fishie to develop fin rot...
ALSO, for a name what about Calcifer (the fire demon) because it matches his colors, OR Stigma which is a Greek letter, but it just sounds cool. There's some ideas. (Why can I name everyone else's fish except my own).