I basically do the same. We are critical development/operational support so I have to have on-call support and do so 1 week at a time with primary and backup (I'm implied 2nd backup if not higher in chain). But my google voice number is only listed on the official schedule website and not in the company contact database so only those that need to know know.

The best thing that ever happened to me was company implementing a lockdown policy so that email/chat/... are only allowed from company assets so I am totally cutoff from work via my phone except through that list and the best part is it by the companies own policy. I only get true emergency calls now.