The last ones I did were all done private. It appears that privacy is offered by default.
(The screen by default shows the privacy version but there’s a button you can use to select your real info. Don’t do that. You’ll get real snail mail from everyone and their brother telling you you’ll lose your domain if you don’t renew with them right now for 45$/year.)
Wholly - IS NOT MY PROMO CODE. Even worse, I don’t get any credit for it. Use WhollyMindless for full credit. I’m really disappointed in someone.