How can I determine if I've set up my phone improperly or if someone is just sending me messages for someone else? [closed]

I would sign out of iMessage on the device and ensure the carrier is only sending messages to that phone number.

Once you've ruled out SMS to the old and new number being delivered, you can re-enable iMessage and test Apple's delivery to that phone.

It's almost certainly a problem with the sender's address book having wrong numbers, but removing and then adding iMessage should clear any mistaken routing if that was the cause.