NINJA ANIME KNOWLEDGE ATTACK!!! KIYAAHH!
The calling out of attack names, in my opinion, comes from these things:
1: The sport of
kendo (the way of the sword), where competitors wear armored helmets and fight with bamboo rods. Basically, Japanese fencing. There is a lot of yelling in this sport, and one can only score points when striking while yelling. It reminds me a lot of anime. This is simply my own observation. I have not read any material suggesting a relationship between anime attacks and kendo, but the similarities cause me to believe that there might be something to it. In the anime "Bamboo Blade", the characters actually yell the official name of the kind of strike or thrust they are making when they compete.
2: Mazinger Z, the first piloted giant robot from anime, and one of the important steps in the evolutionary chain that leads to Transformers. Mazinger was piloted by Koji Kabuto, who would control the robot's various special attacks by yelling them. While in this specific case, Mazinger was controlled vocally, this became the trope by which most all further giant robot shows, and pretty much any other show with any other kind of fighting, would eventually use. From Getter Robo to Fist of The North Star, anime shows have yelling. That's just the way it is. Even the "real robot" show Mobile Suit Gundam has some yelling at times.
3: Manga, the Japanese comics that most anime is derived from, contains big splashy attacks or moves with announced titles, simply as a way of conveying what the character is doing in the form of a static illustrated image. These big, dramatic moments are more effective and exciting to read in a comic book format than reading a series of standard punches and kicks would be, and often show the struggle of a characters will-power as much as they show the particular skill.
4: Anime itself, while having the advantage of showing moving images, has certain limitations it must follow, mostly due to budget. Only a certain number of new animation cels are created for each episode, and so fully animated fight scenes are usually a rarity. The compromise is to show a single dramatic specialty attack instead, as in the manga, and often this will become reused stock footage seen in multiple episodes. These special attacks are interpreted from the manga by having the character yell out the name, giving the character their own special move and adding to their appeal.
There is probably even more to it than this. It's a rather fascinating subject to get into, especially because studying it means watching lots and lots of cartoons.
Sayonara.
