How do I deregister my old number to my new number

You do not have to deregister the old number to activate iMessage for the new number. Simply forget the old number, unless you want to use the same number on an Android device.

First, check to know whether you have an SMS plan enabled at least for One SMS with your carrier for the new Phone Number. Contact your Carrier (Cellular Service Provider) the agency that issued the SIM to you

If your iPhone is used with a carrier not found in the wireless carrier articles, make sure you can send and receive international SMS. (One SMS Only)

See the pic below

4 Step Process --> Turn off and restart iMessage and FaceTime (The order/sequence is very important)

1. Go to Settings > Messages and turn off iMessage.
2. Go to Settings > FaceTime and turn off FaceTime.
3. Restart your device.
4. Turn iMessage and FaceTime back on (Watch the GIF hereunder)