Even though it's strange, technically speaking, Dota 2's name is just that: plain old "Dota 2." Despite its lineage, the proper name of the game is not intended to be an abbreviation for "Defense of the Ancients 2." Valve solely refers to the game as "Dota 2," and you won't find a single reference to "Defense of the Ancients 2" or even "DotA 2" in any sort of official capacity.
Erik Johnson addressed the confusion over the written form of the brand name, citing it as "Dota", rather than "DotA", due to its increasing context as a concept, rather than an acronym for "Defense of the Ancients".
So, I think that while a "defense-of-the-ancients-2" tag synonym could theoretically help someone (maybe?) who couldn't find the dota-2 tag for some reason, it would technically be incorrect.