Blizzard is appealing against Valve for the DOTA trademark, and this case has already gone to the courts. Dota 2 is being developed by Valve has already been in beta for quite a while now, and Blizzard has only recently decided to fight for the trademark. I think this whole deal is kind of stupid. Does the name of the game really matter? It could be called something entirely different and the Dota lovers like myself would still play it and love it anyway.
In my opinion, I think that Blizzard is the bad guy here. All these years when the original Dota was free, Blizzard wouldn't have given a rat's ass to anyone who would apply for the trademark. Now that Valve has made Dota into a franchise, Blizzard wants the trademark all to themselves. I understand that the original Dota mod was built and made on Blizzard's Warcraft III engine, but it's Blizzard's fault for not applying for the trademark earlier. What I think is going on is the work of Activision, they've already screwed up games with so much potential, and now they're trying to do it with Blizzard's games.
I'm just gonna hope that this fight for the DOTA trademark wouldn't affect either one of the Dota games. I honestly would still play it even if it's called something else like "Super Fun Time Party of the Ancients". It would suck to see game development being shut down due to something this redundant, why can't game companies just get along?
Image source: http://kotaku.com/5883938/blizzard-and-valve-go-to-war-over-dota-name