Hiyori is so convinced he's the mermaid who saved the prince (ikuya) when i speculate its actually Haru.
Haru was the one to save Ikuya before Hiyori was even able to form a relationship with him. Haru gave up his tail for legs (when he quit swimming) and lost his voice (lost communication with his friends) plus the official art of only Haru as a mermaid has appeared on screen.
Hiyori on the other hand, is the sea witch. Hiyori is trying everything in his power to keep the mermaid (haru) from getting close to the prince (ikuya), including using a spell (manipulation) to ensure this doesnt happen. He's even gone as far as convincing ikuya to not try to mend the break between the iwatobi gang. Hiyori is convinced he's doing everything to protect ikuya but he's harming his wellbeing.
TLDR Ikuya is the prince, Haru is the little mermaid and Hiyori is the sea witch.