I have had this happen four times over 25+ years.
The first two times were in Edmonton, same lady. Both times it was in West Edmonton Mall. I had been seeing the same MPA for a couple of years, about once a month. The first time I knew that she recognized me, but we both acted cool and didn't acknowledge each other. I saw her professionally a couple of weeks after that and she said that even when she did recognize a client she never did anything because she felt that it was best to keep her professional life and her personal life separate.
The second time was a couple of months after the first. We were both alone, and so I said hello. She responded with a smile and asked how I was doing. I asked if she was busy and had time for a coffee. Long story short, we had dinner and then I dropped her off near her apartment. Definitely an exception to the rule, but at the time we were both single and just looking for some company.
The third time was at a movie theatre in Oshawa. The lady was there with her three kids and a friend (another MPA that I recognized) and her three kids. I was there with my SO and we were all in line at the box office waiting to buy tickets. We all acted like we didn't know each other.
The most recent occassion was about 5 years ago, and it was at the liquor store. I didn't even realize that the lady lived in town. She looked like a very hot MILF, dressed in a halter, jeans and boots. Different make-up, hair and of course clothes then when she was working. I probably wouldn't have recognized her but we were both looking for the same red wine. She asked if I knew where the Lindemann's Shiraz was, and I recognized her voice. When I looked at her face, she also recognized me. We found the wine, she took her bottle, said goodbye and checked out.
Basically, my rule of thumb for these kind of encounters is that unless I get some kind of sign from the lady, I act like I don't know them. If speaking with them I would never use their working name. In the case of the first lady mentioned above, I had known her long enough that I had actual contact information for her, just in case she decided to change where she was working (this was way back in the days before TERB (1984), and no spa or escort agency was going to tell you where an MPA had moved to).
So if you meet someone in public, be cool. Mind your business.