In which fraud may or may not be being committed

Yesterday, I got two confirmation emails from two separate companies for orders that I didn't place. The orders had my name, my phone number, and a former address of mine attached to them. They were paid for with a VISA credit card that I don't own.

So, of course, I immediately pulled up my credit report, and there's nothing there. No evidence of this VISA card. No evidence of so much as a credit inquiry by anyone since we bought our house two years ago. Just to be safe, I put a fraud alert on my credit report and filed an identity theft report with the FTC.

I've just explained the situation to a very nice man at the San Jose Police Department, who basically said, "Well, ma'am, that's weird and I understand why you're suspicious, but at this point we don't really have evidence of a crime being committed." His only suggestion beyond what I've already done was that I contact the companies involved and see if I can get more information.