Your credit card company will be able to deal with the aftereffects of being the victim of identity theft on a number of levels. First of all, by promptly reporting the problem, you will be able to have your credit card company remove charges that were made to the account by the identity thief.
In addition, your credit card company can close down the compromised account and open a new, secure account for you immediately.
Finally, your credit card company will put an alert on your account -- on your new account -- a fraud alert that will provide you with an added piece of protection against the recurrence of identify theft in the future. For example, in placing the fraud alert, you credit card company can additional provide for notification to you if there are charges made to your account over a preset dollar amount. Additionally, the credit card company can notify you if there are any charges made to your newly established account that seem out of the ordinary or deviate from your established use pattern.