This is assuming you are still subscribed to your carrier, you can go to Verizon's website (https://www.verizonwireless.com/b2c/index.html?tab=personal)
to login or retrieve your password. From there you can view the calls you made on your line. You could start from there. Note that Verizon can only give you the phone numbers you call and not exactly WHO you call.
You can try a third party provider if you need matching names and phone numbers. Ive heard of one company like that - lostmycontacts[.com]. Check out their site.