If I change my Apple ID on my iPhone, what are the repercussions and what will happen to calls and messages?

Changing the account will have severe repercussions. Any apps that you purchased on the current account will need to be re-purchased with the new account; the same for music. Your recent call list will be reset. Your backups will no longer be accessible. Anything you synced to iCloud will be gone. Any apps that you have subscriptions to will still need be be managed with the current account, or you will have to cancel them and resubscribe (and pay again) with the new account. And you won’t be able to switch to the new account unless the current account is active and you know the Apple ID and password for it.

For most people Apple ID accounts are for life. You can change the email address for your Apple ID account easily, but throwing away an account and starting over will create a whole stream of complications.