Not sure if you're aware of this or not (I wasn't) but if you are issued a new credit card number the credit card company will automatically update your number to companies that auto charge your account. I recently had a fraudulent charge on my credit card and was issued a new card number (still waiting for the card to arrive) and was surprised to see subscription charges show up now that I have a new card number. They claim that VISA and Mastercard are the ones that do this. My questions is what's the point of issuing a new card number if you are just going to auto update to all these companies?
If you're hoping a new credit card number will cut off subscription charges, beware it won't.