One of the most effective things you can do is let a guy make any choice he wants without making any effort to change it.
I would decide if being kept a secret is something you're comfortable with. If you are, then carry on. If you aren't, then date in abundance until someone stands out as the winner. The guy who is keeping you a secret will see you have boundaries and standards but yet you aren't going to try to change him to make him what you want. He will also intuitively sense competition and he will either step up or fade away. If he fades away, it's for the best.