Removing a device from Find iPhone
Remotely wiping a device, as long as you don't set a lock screen message, will look just like a regular wipe of the phone. However, the person with the phone will have to enter your Apple ID password to use it again.

The reason the phone keeps showing up on Find My iPhone is that your Apple ID is still on the phone, to remove it, all you need to do is wipe it then select remove from account. The person with the phone will not need to enter your password to use it again.