There is many reasons why I don't provide a name when a client books, I would assume it's not far different from jonezy this is the main reason for me though:
1a) I take the booking on in my own name.
1b) A higher paying better booking comes along! But I need to give it to somebody else
2a) I take the booking on and name a different DJ.
2b) I don't get any more bookings... So I'm not working that night
3a) My business takes on the booking, no names!
3b) I'm free to take on that better booking if it comes along and If I don't get booked personally I've got some work!
I always offer a discount for my booking "UK Party DJ" rather than "David Bessant" as the flexability is far greater. Of course if the client wants the personal side of things then they will be guided towards booking me or finding another supplier.