Publicly, Blizzard has kept pretty quiet while Valve has been using the "Dota" name in announcements on their upcoming game Dota 2. What we didn't know is that Blizzard has already
taken legal action against Valve for trying to trademark the name "Dota". Blizzard seems to have a valid argument, stating that the "Dota" (which stands for Defence of the Ancients) name has long been associated with the Blizzard and Warcraft name.
Quote
In contrast to Blizzard, Applicant Valve Corporation ("Valve") has never used the mark DOTA in connection with any product or service that currently is available to the public. By attempting to register the mark DOTA, Valve seeks to appropriate the more than seven years of goodwill that Blizzard has developed in the mark DOTA and in
its Warcraft III computer game and take for itself a name that has come to signify the product of years of time and energy expended by Blizzard and by fans of Warcraft III. Valve has no right to the registration it seeks. If such registration is issued, it not only will damage Blizzard, but also the legions of Blizzard fans that have worked for years
with Blizzard and its products, including by causing consumers to falsely believe that Valve's products are affiliated, sponsored or endorsed by Blizzard and are related or connected to Warcraft III.
Since Blizzard is taking legal action for Valve trying to trademark DOTA (and "Defense of the Ancients", and "DotA", and "Dota"), they should just stick with "Defense of the Ancients".