Regarding the name, I agree with many here. It's a name. It's a fine name. Eventually, people will associate Gleemax with whatever they perceive gleemax to be, and by even next week I think most people will be ambivilent about it. I've tried to encourge people not to waste their ammo on the name, since it almost seems like a feint, and I think there are more legitimate topics for the community to discuss and make their voice heard on.
As far as what the Digital Initiative is, we've done a terrible job of making that clear. And I think a lot of it is my fault. I can even say that WotC D&D folks, like Scott Rouse and Chris Perkins, expressed concern about refering to what we're doing with D&D as the D&D DI, so I can't say I wasn't warned.
So here it is: WotC has a Digital Initiative. Gleemax is going to be the home for gamers. RPG, TCG, BG, Minis, you name it. It should be the place for anyone interested in anything to do with any tabletop or strategy game to come and find what they want. It could be people who can describe that game, extra content for that game, people to discuss that game with, people to play that game with, it could suggestions on what other games they may like, even links to other sites, etc. As part of this, Gleemax will have a large amount of features and tools to help facilitate the community.
D&D also has plans in the digital space. These are brand specific but will certainly be supported by a lot of the basic Gleemax functionality. We haven't released a lot of details on the D&D DI because we expect to make some big announcements when we're ready. I can't say when those announcements will happen. I will continue trying to wheedle out the bits of information I can from the D&D folks, but it's extra hard at this time of year, with all the preparations they're making for Gencon, which has always been a pretty big deal for WotC and D&D.
edit: Changed their to they're and strategic to strategy (strategiary)