No.
While I didn't (don't?) mind RealID in-game(I only invite people I ACTUALLY know, aside from a couple of people I've gamed with for YEARS), I do NOT find it necessary to have my name on display so that every asshole with no life could POSSIBLY decide to start something with me--especially since I'm a woman.
I allow a small group of folks online to know who I am, and I'd rather keep it that way. TBH, once I discovered that Blizz and Facebook teamed up, I changed the few privacy options I'd left slightly opened to completely unavailable. I hadn't planned on linking my FB to battle.net, I hadn't even visited the Blizz site there, but now I REALLY won't be doing much beyond playing the game and buying some swag occasionally...
Hopefully Blizz listens and changes this, cos some of us used the tech/cust support (and realm) forums every now and then, and after the new policy goes into effect, we could be out of tech/customer service support due to the fact that we don't want to put our name on the troll-infested forums.