iPhone 6 not creating contacts correctly

Hi everyone,

I'm trying to add new contacts to an iPhone 6. After adding a new contact, the name will show up in the recent calls list and in text message, but none of the contacts are showing in the contacts list itself. So, the names are definitely being saved to the phone, they just aren't being added to the contacts list for some reason.

Edit: I should add that this is a brand new phone.

Any suggestions would be greatly appreciated, thanks!