I know everybody wants to guess Monstro but I actually think he might be the Frog Prince (Not the Disney verision though). Could explain his womanizing nature. Also, apparently in that story the Prince was cursed da a fairy and he was hanging around the Blue Fairy's character in the finale quite a bit so who knows.
I think he might be Monstro. Judging da that he's always around the Blue Fairy and the Blue Fairy had to save Pinocchio from Monstro. Also Dr. balena is always seeming to be "swallowed up" da the problems surrounding him. Maybe Dr. balena was like Jiminy Cricket before Jiminy was a cricket. A sudden transformation might have occurred. Dr. balena is also a bit of a lech so maybe he could be male siren sort of creature. I don't know if that makes any sense. He could be also Captain Ahab from Moby Dick. Captain Ahab was always after the famed white whale. Dr. balena wears all white in case anyone hasn't noticed. Maybe he's not Monstro o Captain Ahab. Maybe he's Moby Dick. He's a very shadowy figure; lurking in the dark ready to appear out of nowhere.