Here is what I think is going on with that SIM card:
You had a cellular service plan for a tablet from your carrier. Your carrier assigns the caller ID to your account / phone number. Your iPhone does NOT assign the caller name to the device. You then switched the SIM card to your iPhone. When you make a call using that SIM card then the original caller ID shows up at the recipient's end.
I am not sure whether your carrier allows a data SIM card for a tablet to be used in a cellular phone. This is because the cellular phone plan is more expensive than the cellular data plan for a tablet. I recommend that you contact your carrier and sort this out including the caller ID issue that you are experiencing.
Axel F.