I'm going to offer a somewhat different perspective.
Everyone googles everyone. Not just escorts and clients, but co-workers, bosses, childhood friends, neighbors, in-laws etc. Whether that makes them stalkers or not is not the point. Everyone does it. So please if you're an escort who cares about hiding his real identity don't post the same photos in your profile that you post in your other social media accounts. If you do people will find out. And it's not only clients. A lot more people look at those sites than the guys who actually hire, and they all are vey capable of doing a simple image search. Welcome to the electronic age. Once you put your picture out there it's in public domain. So choose wisely! It's in your control until you put it out there.
Now as for the OP, I think you should tell him and here's why. He's either aware of it and won't care or he is not and will be grateful that you've told him. The worst case scenario is that he doesn't want to see you again, but at least he'll be aware that his own privacy is easily compromised.
12 hours is a long time and if you accidently divulge something, it will definitely make you look like a stalker, not to mention that it would almost guarantee that he doesn't want to see you again. Plus will you be able to relax and have a good time while constantly being cautious of everything you say?
Option three - if you do go through with it and don't say anything, then he continues to live under a pretense that he's identity is well guarded when in fact everyone in the world can easily figure it out.
For me personally knowing an escorts real name makes me very uncomfortable and regardless of if I've hired him previously or not I will tell him. If that makes me a stalker so be it. I know I'm in minority but it's just my two cents.
Finally we often see this question but we rarely hear from the escorts. So here it is guys: If someone found out your real name would you want them to tell you?