Can a person request his/her credit card company to temporarily stop payments to a specified company?
This is assuming that the person does not have autocharge (or autopayment) with the company. Can the person request his/her credit card company to stop the payments?

The easiest way, and the least likely to get you accused of fraud, is to call the credit card company and report your card lost or stolen.

Two things you need to realize, 1- the card number will change so any auto payments will get returned unless you notify the companies of the lost card and new number and 2-if you have a legal agreement with the company that is charging your card monthly, odds are you will get nailed with a NSF type fee, which could be more than the payment.

Call the company directly and ask to temporarily suspend the service/payment.