I only really tack the PhD on when I'm emailing vendors. They'll withhold technical information if they don't know that you're in a position to need it, so it helps.
Internally, everyone has a PhD, so it really doesn't matter. Nobody goes by "Dr," except for the nameplate on the door (which I still get a little warm and fuzzy seeing). You'd come off as a huge dick if you insisted on going by Dr Lastname, even to your postdocs.