Why does my refurbished verizon iphone 4 say sprint next to carrier in my settings?

Yeah and I spoke to Verizon over the phone and they said the phone is verizon or else they would not be able to see it on their end. And they said they activated the line. But the phone is not activated and the carrier says sprint under settings although Verizon says it is a verizon phone

It's possible that it's actually activated but during the refurb process, they totally forgot to reset the phone to factory level. AKA someone else owned the phone before you and Jailbroke it. When you Jailbreak your iPhone, you can put whatever carrier name or name period you want up where it says the carrier among other things. I would send that phone back and request another one, especially if they're denying that there's any problem with it.

Also what could've happened is, they could have had someone switch to their service from Sprint and trade in the iPhone. Even though it went through a refurb process, there's absolutely no possible way that Verizon can change the original carrier. IPhones are locked to their carriers or CDMA. That means if you buy an iPhone from Sprint, you can't use it on any other carrier EVER. It's 100% LOCKED to Sprint.

So yeah, definitely report this issue to customer service or who ever handles refurbished devices and tell them you need another one. There's clearly a mistake on Verizon's part and they have a hard time just in general admitting that it was their fault.