What is the Concept of Ownership…
You own your phone number, in a sense, as long as you pay for it. When you allow your phone service to lapse, you probably have a certain amount of time to pay up if you want to keep your number. If you do not, the ownership of that number can then be passed on to someone else. This is happening in shorter and shorter time frames today, as phone numbers are in high demand due to soaring cell phone ownership.
That being said, what happens when you get a phone call, and you want to know who owns it? Do they own a number in the sense that they could be prosecuted based on the ownership of that number if they are doing something wrong? What if they have scammed you out of money? What if they have done something to hurt your children? What if they have interfered in your marriage? Would they be so quick to claim ownership of a number then?
Along the same lines, when you call someone with your mobile phone, you are taking ownership in that number, though you may not want the world to know what that number is or that it belongs to you. What is great about mobile number ownership, depending on your perspective, is that they are more private and much harder to find and/or trace.
That does not mean it is not possible. If you want to know who owns a telephone number, you have to know where to look. You can try free sources, but you may not get very far with those. When you have to know about ownership of a number, use a phone lookup in reverse to get the information that you did not have before.