DOTA stands for Defense of the Ancients. It was a Warcraft 3 Mod that got super-popular. League of Legends and Heroes of Newarth are both stand-alone DOTA clones. So the guy that designed the original WC3 mod was hired by Valve to develop a new stand-alone game (lacking any Blizzard characters/branding) called DOTA2. Then Blizzard decided to make their own DOTA game using the Starcraft 2 engine called Blizzard DOTA. Blizzards game is going to feature various iconic characters from their games (Thrall, Arthas, Jaina, Jim Rainor, etc). It's basically going to be like Blizzard Smash Bros.
I dont really see what grounds Blizzard has to make a stink about the name. DOTA is an abbreviation for a mod of one of their games. Its not like Valve is calling it Warcraft: Defense of the Ancients 2.
Ohh gotcha. Name reminds me of the WoW bg Strand of the Ancients.