I have one SP who has become a friend. We know each other's real name, and I think it would be ok for me to approach her and say hello. If I am with my SO, I would have some difficulty explaining where I met this lady. I belong to a couple of business groups outside of our provider-client relationship.
My friend gave me a gift not long ago, which I keep in prominent place in my home. I explained the connection by telling my SO the gift came from a friend in one of those business groups. I would introduce her as the friend who gave me the gift. However, I think the SP in question has enough sense not to approach me if I am with another woman.
I have recognized one higher priced SP in one of those groups. I have been tempted to speak to her at one of our meetings... when I can do so in private... and tell her I recognize her, and ask how she would feel about doing some personal business. I could also call her and tell her of our connection prior to making a date, and let her decide if she wants to make the date knowing of that other connection. Regardless of what she decided, I would then follow that up with a face to face introduction at a meeting, just so she knows we both have a need for discretion.
In any case, as has been mentioned in this thread several times... discretion is the better part of valour. Unless you know the SP personally, DO NOT SPEAK TO HER, or CALL HER BY NAME. "Marylou" may not be her real name, and you could cause her major embarrassment if she around others who do not know of her extra-curricular activities.