Is the other person also on Verizon? Are they both Android's? Not that it matters entirely what kind of phone it is... I've switched phones on my plan in the middle of a contract with absolutely no problem at all; you don't even have to talk to anybody at Verizon, just activate the new phone on your plan and tell it which line you want it on (even easier if you only have the one line).
There is no charge for switching phones, and adding or dropping a data plan is also possible at any time. The only thing you probably won't be able to do is get insurance on the phone, given that they can't vouch for the quality of it.