Find My is disabled

It is likely identifying as your old iPhone because you have not changed the phones name.

Open the Settings App

Tap General

Tap About

See name and the top and change the name to how you'd like your phone to be shown

I assume that your phones have different names. On the new phone.......

Tap Settings

Tap [Your Name] near the top of the screen

Tap Find My

Tap to turn Find My on

On your old phone......

Do the same and tap to turn off Find My

The old phone has been erased. I'm willing to bet it's as I suggested and the name wasn't changed on the new Phone in About.

You're very welcome!