I would ask him if he gets the full name and phone number etc.  from the lady at the DMV, his doctor, the guy that fixes his car, the waitress he gives a his credit card to, the loan officer at the bank, etc.?

You are the business, you get to have the information required to run your business, and to protect yourself.  You are the one that will take the brunt of anything from LE, you are the one at greater risk from assault and victimisation, you are the one accepting greater risk, if a client doesn't understand or accept that then, even if his real name were not an issue, I would suggest against seeing him.

Screening is how you manage some of your risk.  It is not a symmetrical relationship.  In this life you have to be able to let some customers (people) walk away.
 If he needs that information to manage his risk then wish him luck finding someone who will meet his needs, but you're not it.  My opinion is that he is messing with your head and that this is a microcosm for other issues that will arise.
 Good luck getting started.  Where are you located?  Can you give a link to your website or which local boards are you advertising on.
B

Protect your interests and identity, no matter what.  Assuming you are indie, who else do you have in your corner besides you?

Real hobbyist know how the game works and would not ask you such questions.  Just last weekend, two providers I know and had been with asked me out for drinks/dancing to celebrate with a friend of theirs.  It was totally non-hobby and public, but at no time did they reveal their true names to me. It is just understood that is part of the process.

This guy is setting you up for problems down the road.  Move on, do not look back