"Credit monitoring" is not only pretty much useless, it is a scam to try and get people to sign-up for a very profitable service. Most of them have draconian "auto-renewal" after the "free trial" or "free year" and they count on people forgetting to cancel and or being scared. The services can't and don't stop any abuse, but just allow you to SEE what is on your credit report and some will attempt to notify you when it is accessed. Both require you to take quick action, do something, fight things, etc.
If you really want to protect your identity and credit, then it requires "locking" or "freezing" your credit reports. That didn't used to be possible, but now it is. But rather than making it easy and centralized, one has to enroll/setup AND pay about $10 to each of the 3 agencies.
http://clark.com/personal-finance-credit/credit-freeze-and-thaw-guide/Of course, you then have "thaw" them if you ever apply for credit or need your credit score checked by any company that requires a credit check before opening an account or doing business. That even means things that have NOTHING to do with opening a new line of credit, for example: enrolling in cell phone service, opening a bank account, being hired by some employers, getting certain types of licenses, getting utilities turned on (water/electric/gas), etc.