Originally Posted by Often1

This does no good. A new card is not a new account. Additionally, the downsides may be quite significant.

Charges coming from legitimate suppliers are simply transferred to the new number, the same as is done with expired cards.

This is a good way to wind up on the rental company's DNR list and when it becomes apparent to the card issuer (bank) what you have done, to have your card flagged for potentially fraudulent behavior.