Why can I still receive text messages when I get a new iPhone and an old iPhone?

Because the iOS of Apple's mobile phone needs account password login to be fully used, that is to say, your old mobile phone has not logged out of your Apple ID, but logged in to a new mobile phone. Two mobile phones log in to the same account at the same time, and the information will of course be received. You can re-register an account, or you can use an account together, no problem.