IceFrog was on the Dota2 team, and valve owns the trademark

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.

It's also worth noting that the original TTD had nothing to do with the original Atari and a lot more to do with Microprose which was purchased by Hasbro Interactive, which was later purchased by Infogrames which renamed itself Atari after buying the remnants. Oh, and the "new" Microprose has even less to do with the old Microprose than the new Atari does with the old Atari (at least they own the rights to all the old Atari titles).