When I first got married, I changed my name legally and (eventually) on my driver's license. I did not ever get around to changing it with my credit card companies. While I did change my name with my bank, I haven't gotten new checks or a new debit card. In other words, I have two recently acquired credit cards with my legal name on them, and several credit/debit cards without.
The frightening part is, nobody has EVER called me on it. I didn't update my name on my driver's license until about a year after I got married. In the intervening year, I used my driver's license as identification for all kinds of official things. The fact that my ID didn't match my social security card was never brought up. Since I changed my driver's license, no merchant has ever asked why the name on my credit card is not the same as the name on my ID.
So, I guess the moral of the story is that women can steal the identity of any other woman with her same first name. It will be assumed (I guess) that she just hasn't changed her last name with all her credit card companies.