For someone to trust them with personal information

No matter how well established you are, and some will give it up at the drop of a hat. Many hobbyists fall in between where they are willing to give it up to some providers but not just any provider, but it's at their level of comfort. There is no hard and fast rule as to what makes a provider well established "enough" for someone to give up their info.  

or any other form of employment where you could loss your job if discovered (or info used to blackmail you), then you would be more reluctant to give out personal info.

If you read enough reviews and follow the discussion boards, you can usually tell which providers are flakes and which have a good business sense and can be trusted.

How that worked when some providers are screening. I know everyone has different methods.

I say that a providers level of establishment doesn't matter at all.  If the provider feels comfortable and safe enough to see someone, then I'd say the level of information she requested was just the right amount for her.  If the client was not willing or doesn't feel comfortable with the level of disclosure a provider requires, then no hard feelings...I'd say it was a mismatch.

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I'm a provider and I can only speak for myself.  

Newbies are always reluctant to give up the personal information (real name, employer, etc). I always tell them that the trust goes both ways. I value your privacy as much as I value my reputation. If I were to "out" you to your work or wife for no good reason, you could come here and every review board possible and tell everyone what I did, and then NO would see me again. My business would be dead. My reputation would be mud. So, don't abuse, rape, violate, etc a provider and we will not out you. Simple. Why would we abuse your private info when we know you can ruin out reputation and business? The trust goes both ways. We trust seeing an unknown newbie with no provider references and you trust we won't out you.

Reviews are your friends...read them if you are considering meeting someone new. Use your own judgment, though, over the advice of others.