It's far more complicated than that and ended up in court. They own the commercial rights after a legal battle with Blizzard (and Riot was in the fray, somewhere), who retained some rights to the name. Valve's 'Dota' doesn't legally stand for anything because it'd be a direct reference to Warcraft 3 (Ancients), just as TTD can be said to not legally stand for Transport Tycoon Deluxe.

That's the entire point that you've simultaneously acknowledged and missed.

IceFrog didn't start DotA, either. He had no claim to the name.

TL;DR there's complicated history behind it and much money was spent arguing over it.

IIRCC, Eul, the guy who made Dota originally, also works at Valve.