Baal and Beelzebul were two twin gods. They won the Archon War together, and when Baal established the Shogunate, Beelzebul became her Kagemusha (Japanese: 影武者 “shadow warrior”). In other words, she acted as Baal’s body double. As far as the world was aware, there were not two, but one. They complemented each other, and they ruled Inazuma jointly. So there was no need for the public to know the truth. The name “Baal” and the title of Raiden Shogun was understood to refer to both of them.
According to Yae Miko, while she was not close to Baal, based on her first encounter with her, she found her to be a kind and gentle god who disliked violence. The Musou Isshin, the sword that now belongs to Beelzebul, was originally Baal’s, and when Baal owned it it was never sharpened, being simply a symbol of true peace. She enjoyed spending time with Beelzebul and was known to be very relaxed.