I can't recall ever being asked for a photo ID prior to a session, but I don't see any problem with showing it - "here's my photo and here's my age." Done. I doubt that a mistress would record or even remember my name.

I do get annoyed with hotels that made a copy of my driver's license along with a credit card when checking in, but that's more about having to take my license out of my wallet rather than just showing it. And I think that I would be hesitant to allow a BDSM provider to make a physical or digital copy of my license. That could get into the wrong hands.