Is it permissible for me to keep a young man's number with the intention of contacting him in the future for marriage, with the knowledge of his family but without the knowledge of my family?

You have done well by repenting and ceasing communication, for the temptation between men and women is great, as narrated by Al-Bukhari. There is no need to keep his number as long as your family knows him, so do not open a door to temptation for yourself. The Sharia came to block pretexts (means to evil), and the doors of Satan must be closed in obedience to His (Allah's) saying: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing. And if not for the favor of Allah upon you and His mercy, not one of you would have ever been purified. But Allah purifies whom He wills, and Allah is Hearing and Knowing."