I think one reference should be sufficient. If you're able to confirm that the lone reference is indeed a provider that has seen the client, what more do you need to know?
Asking for my real name and place of employment is an absolute deal breaker. I've encountered providers who mandate that because they see the client at their home. That's understandable, but that's not for me.
In the end, I think everyone has taken a leap of faith at some point. Clients have seen providers with no reviews, and providers have seen clients without checking references or even asking for them. It makes the world go round, otherwise you'd run out of both clients and providers.