If you happen to find a brand new phone?

Yes, Verizon knows who it sold the phone to.

They would probably not tell you who that is but if you are willing to leave your contact info, they will tell the owner how to get with you.

You should (hypothetically) turn it on (charge it if it's dead) and go into the contacts. Find something like "Mum" or just pick a random name; ring it and let them know you've found this phone and ask what you should do with it or if they would like to come and collect it off you. So basically, do the right thing. If you can't do that then hand it into your local police station or one near where you found it but keep hold of it for a few days in case you notice someone come by looking for it.

Sure, nothing is stopping you from selling or keeping it but that's a bad thing to do and (hypothetically) you'd feel guilty. (And even if you kept it, you'd probably be caught eventually).

You could find the owner be calling someone on the contacts list and asking them how to get their friends phone back to them.

If the owner tries to locate the phone through GPS or the police station it will be redirected there once you activated it just relax and explained what happened and then try calling his/her contacts and explain to them one by one

if it is not password protected go to recent calls and call one of the recent numbers. they are usually more reliable people to help you find the owner.