Getting new credit cards after a divorce can be tremendously difficult, especially if your wife didn't maintain any lines of credit under her maiden name. Not knowing the details of your breakup, I'll can only assume positive intent here. Like many other women in the same situation, your ex-wife may have discovered that an instant approval credit card application will go through much more easily if she enters in her "old" information, then changes the details after receiving her new account information.
If you have a relatively cordial relationship, she's probably picking up her new cards or statements from you directly. After a few months, there should be enough data on her credit file confirming her new name and address to make all of this moot. If the whole thing makes you uncomfortable, you can ask her to stop. (Besides, she's technically providing false information on her applications.)
On the other hand, if she's using your name or Social Security number on any of her credit card applications, she could be putting both of you in serious legal and financial jeopardy. Since most credit card applications are now automated, it's rare for a bank to collect an actual signature when opening a new line of credit. Your wife may know enough of your personal information to fake an e-signature and to pass a standard identity verification request. It's not hard if she knows facts about your life, like the name of your high school, the bank where you held your mortgage, or any of your previous addresses.
If you're an unwitting co-signer on her new account and she defaults on a balance, the bank will hold you liable for that amount unless you can prove that you never opened the account. It's possible, but time-consuming and possibly expensive, to get a bank to let you off the hook for your wife's bill.
If you're worried about this happening at all, consider placing a consumer credit block on your files with each of the three major credit reporting agencies. The block won't affect your credit score, but it will basically require a bank to connect with you in person when considering a new application. It will also prevent anyone else with access to your personal information from opening up a new account.