I can understand both sides really....that having a small friend group you'd want to develop that bond into something more tangible than screen names, but equally, knowing that he was reticent to hand out that information, that it was something he wasn't completely comfortable with. The fact that you describe it as hard to obtain shows that you were persistent, and he was reluctant, so it seems clear that you knew he regarded it as privileged information.
You blurted it out by accident, no harm intended, but if he was sensitive about it being shared that's two issues for him...his name being shared publicly and your breach of trust. Personally I'd probably send him a message explaining how you feel and that you understand he's angry but you don't want to lose him as a friend, and then just wait. You can't make him forgive you but if he understands that it was an accident and that you don't want to lose him as a friend, then perhaps a little time will help him accept that mistake.
Also, you don't know he hates you....maybe he's just a little disappointed in you and he's reassessing your friendship.