Is he normally shy about asking for other things? For instance, if he's hungry or thirsty will he ask for food or water? Or is it just going to the bathroom that he won't ask for?
He told you that he doesn't want people to know that he pees? Did you ask him why he doesn't want people to know? The irony is that if he actually pees in his pants people are definitely going to know, and it's going to draw a lot more attention than just going to the restroom.
I'd call his pediatrician just to see if they have any ideas. But in the meantime, if he's going to act like a younger child, then you have to manage it the same way. Remember when our kids were toilet training and we had to tell them go frequently so that they wouldn't have accidents? Do the same thing. When you're driving somewhere, take bathroom breaks and insist that he use the bathroom. If you're in a restaurant or a store, show him the restroom and tell him to use it. .Don't say it in a way that will humiliate him, because that's not the point. Eventually he's going to get annoyed at having to go so often, and you can then explain that you don't have any other choice because he refuses to tell you when he needs to go.