Just like hotels will if they are suspicious..
Get the hobby phone or that Google voice. I personally would just get another phone.. those disposable services are too cheap not to. Mine is $60 a month with unlimited everything and data plan for the net. My hobby emails are synced so I can keep up with inquires.
I Google my clients so yes other are Googling for sure. You'd be surprised what you can find by just a phone number.. My hobby # is not listed anywhere either so it cant be searched. Even my website is not searchable. I pre-screen to get my link and #.
I really dont worry as I have a day business and wont be applying for a job anytime soon but less info out in the open less chance of people finding out. I advertise to a direct market.
And people make your FB private, even if you're in a search they cant see your info.
You search me and only a page to request me comes up, no other info.