@Meowmix is correct in regards to the call display working fine on unlocked devices and this is something we can definitely look into for you. If you haven't already called into technical support, I have sent you a private message to reply to, from our @CommunityHelps. You can click here to access your inbox or click here to learn more about our Private Messaging system.
Ok, that seems good.... As an aside, does the iPhone 6s/6s+ have VoLTE support as well? I made calls that looked like they stayed on LTE on my 6s+ a few times but I wasn't 100% sure.
You can determine if VoLTE is enabled on your phone by the following steps;