You’d probably know these names from Naruto, but they are actually from the Japanese Mythology of ancient deities. They were birthed from Izanagi who, with Izanami were responsible for the creation of the Japanese archipelago. But the creation of Japan would be a story in an entirely different article.
So Amaterasu came from Izanagi’s left eye and was the incarnation of the sun. Tsukuyomi from the right eye was the incarnation of the moon. While Susanoo from the nose was the incarnation of the storm may it be wind, sea or even sand.
Amaterasu became the sun goddess of Japan and was given the heavens from Izanagi. So maybe being daddy’s little girl, you could say that she was given the best inheritance from him. Now, Tsukuyomi was cool with the decision and when he got to the heavens, he stayed there with his sister.
Susanoo on the other hand, became infamous for his rivalry with Amaterasu. That is apparent when the duel of “who could create the best creatures” came to no conclusion, Susanoo went on a rampage. He killed and skinned Amaterasu’s pony and thus hurt her feelings so much she went and hid in a cave. This caused the sun to disappear for a very long time. This incident caused Susanoo to be banished from the heavens. And after some time Amaterasu just went back to being her old self.
Now Tsukuyomi and Amaterasu were always on good terms until one day, Amaterasu asked him to go to a feast hosted by the food goddess, Uke Mochi in her stead. During the feast, the goddess made food by regurgitating them out. Fish, game and rice was all projected out from her mouth. As the last bowl of rice was coughed out, Tsukuyomi was very disgusted by the whole thing that even though it looked extravagant and exquisite on the table, he killed her.
Once Amaterasu learnt about the incident, she was so mad at Tsukuyomi that she refused to ever look at him ever again that she moved to a different part of the heavens. Apparently this is why there is day and night.
Want to know about the creation of Japan? Read about it here: Izanagi and Izanami in Japanese Mythology.