How about a field in the provider profile that reads something like "requires real name for screening" or even something simpler like "verification site friendly" with a value of yes or no. Clients who aren't going to provide real world info could screen out providers that require it, saving the client time and the provider some aggravation.

You know, right up front on their websites and/or ads?   I'm not being a smartass;  I'd genuinely like to know.  

The percentage of providers for whom real-world info is an absolute, non-negotiable MUST is fairly low..... how many of this group have you found that did not alert potential clients about that in their advertising

To date I have found none that do not tell you upfront  
Add to that you are someone Iwould love to see but will not give up that information with all the issues here in our area/
Your name  requirement may even add to your allur