As of today, it turns out Valve has those rights. The two giant companies have amicably settled the issue amongst themselves. Valve will release its DOTA title as Dota 2, and Blizzard will release its as Blizzard All-Stars. Personally, I'm a bigger fan of All-Stars, anyway. It gives the name some real flavor and, as stated by Blizzard VP Rob Pardo, "ultimately better reflects the design of our game."
Of course, regardless of the decisions made here, the fan community will inevitably continue calling this genre of games DOTA or some variation thereof. If you care to read the full press release regarding this agreement, hop behind the cut below.