The Japanese rolled omelet commonly served at breakfast is tamagoyaki.
Tamagoyaki is made by cooking thin layers of seasoned beaten egg and rolling each layer over the previous one. The result is a compact rectangular omelet with visible layers. Seasonings can include sugar, soy sauce, and dashi, so the flavor may range from sweet to savory.
The omelet is cooked in a rectangular pan called a makiyakinabe, although a standard round skillet can also be used. It is widely served in Japanese home cooking and appears in bento boxes and sushi restaurants as well as at breakfast.
Dashimaki tamago is a closely related style that contains more dashi and is generally softer and more delicate. The terms are sometimes used loosely, but tamagoyaki is the broader familiar name for the layered rolled omelet. Okonomiyaki is different: it is a savory pancake containing ingredients such as cabbage.