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According to a pair of legal filings, it appears that Blizzard is suing Valve to prevent it from trademarking the DOTA name. Blizzard claims that the DOTA name has been closely aligned with the Warcraft series for the past seven years. Defense of the Ancients was originally created as a mod for Warcraft III.
1. By this Opposition, Blizzard seeks to prevent registration by its competitor Valve Corporation ("Valve") of a trademark, DOTA, that for more than seven years has been used exclusively by Blizzard and its fan community, under license from Blizzard. By virtue of that use, the DOTA mark has become firmly associated in the mind of consumers with Blizzard, including to signify a highly popular scenario or variant of one of Blizzard's best-selling computer games, Warcraft III. Over the past seven years, the mark DOTA has been used exclusively in connection with Blizzard and its products, namely Warcraft III. Most notably, DOTA has been used as the popular name of a Warcraft III software "mod" file that has been distributed, marketed, and promoted by Blizzard and its fans (under license from Blizzard)
Read the legal documentation here.