You can give them a different phone number, which the guidelines suggest and which I can do because I have a google voice number. So I have 3 phone numbers (landline, regular cell no., google no.). I also change my google voice number from time to time so I can give a totally different number.
I've done both the inquiry-only shops and the rent/reveal shops over the last 2 years (2 of each), plus did one about 5 years ago, and actually did rent for about a year at one location. I've never had any trouble going through the scenario. With the inquiry-only one, I give a fake name. On the rent-and-reveal ones, nobody has ever found me in the system, to the best of my knowledge, and have always been surprised at the reveal. I don't believe I've never had to give my DL any any of these shops.
I learn something new every day, but not everyday!
I've learned to never trust spell-check or my phone's auto-fill feature.