Some tips for trying to avoid this kind of BS (low tech but helpful)...

I'm going to differentiate between "credit card fraud" and the much worse "identity theft/application fraud".

Let's start with credit card fraud. It happens when someone uses a credit card that you actually applied for, e.g. they physically steal the card and use it, or they get enough information about the card to pretend to be you using it, e.g. order stuff online or use a clone to swipe. A third gray area fraud occurs when an unethical merchant loads a recurring charge onto your card, technically informing you in small print but not really being very upfront about it.

The biggest hassle for the merchant is a big purchase, but for you, that may be the least hassle, because you're likely to be notified.

At any rate, the best way to prevent any of this is to follow what's going on with your credit cards. Just create an account at the bank that issued the card. Not the credit card company; they collect fees from the merchant but the bank is lending the money and keeping track of your account. If it's a Chase card, for example, create a Chase account and check on the card pretty often. Its easy, so once a week is reasonable. If you see any charges you don't recognize, deal with it immediately. Obviously use an adequate password and don't share account details with people you don't trust. Set it up so that you'll get an email or text warning if someone changes the password. However, for the most part, it's hard to go wrong.

A much more aggravating situation occurs is someone gets enough information on you together to open new accounts in your name. You won't get the bills - they'll have them sent to a fake address - but when the bills go unpaid your credit rating will tank. And lenders may pursue you legally.

First I'll tell you how to make sure that isn't happening, and then I'll tell you how to try to prevent it from happening.

To make sure it isn't happening on a significant scale, sign up for credikarma or some similar online service. Creditkarma is legit and seems to work quite well. Check in once in a while and make sure that all the accounts on your report make sense. Also check the credit inquiries. Make sure they make sense too.

Okay, but what if you do discover something? What if Dale Buford with excellent credit lives in Tennessee but he suddenly sees that a car loan account for a car he didn't buy has opened? And a credit inquiry has come in from a car dealership in Minnesota? You don't want to get to that step, but if you do, you at least know what's happening and can try to get on top of it. https://www.identitytheft.gov/ The lender may not be your friend, by the way. Their position may be that they used due diligence and identified you as the borrower and you owe the money.

Unfortunately, and I don't know if this happens, there is hypothetical low level identity theft that might be hard to catch. If, instead of buying the car, the thief just uses your name to set up utilities on an apartment, you might not even see a credit check. Or you might just see a hard to figure out credit check. Utility companies usually don't bother with much credit reporting or collection agency stuff, because if the bill isn't paid they'll just turn off the utility. It can still burn you though. Imagine if Dale later moves to Minneapolis and when he tries to get the lights in his new place turned on, they tell him he has an unpaid Minneapolis electric bill.

You want to avoid it by using prudence - don't give out more information than is necessary. Yet even the most prudent person could be fucked over by a dishonest health care or financial services employee. So the best bet is a combination of not taking too many risks, combined with checking to make sure nothing fishy is going on.