Changed Iphone's name, but it is not changed, when i am tracking Apple Pay transactons with the bank

Yes if you sign out of your Apple ID, all of your cards will be cleared and you will have to add them again when you log back in.

I would suspect that your bank identified your name when it verified your card and the name of the device is not sent to your bank with every transaction. I don't know if you would have any luck contacting the bank for a device name change, but you may be able to update the name by removing the card and adding it back again.

When the bank verified your card and issued the token, it was given a name. As a security and safety measure the token is not updated. Logging out of Apple ID, as Jim suggests, will remove all your payment methods from Apple ID and and when you added them again and go through the verification process, the device name should be reflected in the new token issued.