Hello and welcome!   Well, let's make this as simple as we can . . . you're going away to college and want your own account which you will pay for yourself I presume.   Ok, the best way to do this is through an Assumption of Liability (AOL) in which the Primary Account Holder (one of your parents I presume) needs to call verizon (peferrably with you nearby the phone as well) so that the transfer of the account can take place.  

The Primary Account Holder needs to first authorize the release of the line to you.   You will then acknowledge acceptance of the line.   I must tell you that you need to have established some form of credit as you need be what verizon calls "credit worthy".   If accepted, the line and phone number will be placed totally in your name only and you will be responsible for the payments.

They will NOT let you just drop out of a contract (family share or not) and just start all over without Early Termination Fee (ETF) penalty.  However, if you got this line/phone last August then come this August (one year point) you become eligible for a "One Year Upgrade" (discount) on new phone!   You'll have to be a "My Verizon" member and be on a plan of $49.99 or more (which your family plan probably is) and be willing to signup for a two year contract.    I hope this helps