Not a rival per-se but its close alcantarilla, she's Kanami Mashita. She was revealed in Persona 4 Dancing All Night. She was the girl that replaced Rise after she left her agency I believe. Correct me if I'm wrong though. :)
Kanami Mashita is the lead idol of the Kanamin Kitchen idol group in Persona 4 DAN, which is what this doujinshi is based on. They promote her/talk about her briefly in Persona 4 during Rise's break but Rise goes back to being an idol after P4G events and the fighting game.