Do it on yourself. Pay for Intellius or one of the other services to check. That's what most companies do. Very few companies are able to do much more detailed than one of the public services.
Standard background checks sift through public records - car purchases, utility connects/disconnects, credit card histories, criminal records, etc.
There's no way to connect you to the hobby if you a) don't use your credit card with a provider, or b) you don't let anyone connect your hobby name to your real name (like using facebook to friend your providers and not make it private).
If you are worried, always use pre-paid cell phones and pay for the extra time with cash. You can track a credit card purchase back to a phone line if you want to spend the time and money to do so.
Private employers typically use a search service to do a standard background check. It's all automated, quick and cheap. Higher-level positions might employ a person to do a background check, just as many government positions might, especially if they require any sort of security clearance.
And remember that the internet never forgets anything! Once it gets out chances are its gonna be archived somewhere. So play it smart and don't do/say anything stupid that can connect your alias to your real name. If you do these steps then chances are you are safe.... unless the SO hires a PI with a camera...
Just went through the FBI / TSA background check required for a Transportation Worker Identification Credential (TWIC), because some of our facilities are inside "designated port areas". Been hobbying a long time & passed the check with no problem.