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What do you think about Valve attempting to copyright a name that 'belongs' to a previously free game mod, for a game they don't own, and then selling that game for profit?

That makes it sound pretty bad, but, it's what's going on. Word is that Blizzard is a bit pissed about it, but I don't think there is much they can do about it besides file a counter claim.

I've also heard people suggest simply changing the name of the Valve version.

In my opinion, Valve beat Blizzard to the punch, so they have no right to complain. Besides, since Blizzard paired with Activision, I don't have much respect for them anymore.

I still greatly respect Blizzard honestly despite the Activision thing.Activision really doesn't meddle in Blizzard's affairs too much. Blizzard also takes good care of their customers. Either way valve should consider their copyright things a lot more carefully to avoid scandals like this.

Blizzard still has the sort of mentality that pleasing your fans earns you more money. Activision is purely bureaucratic in their approach. Companies like activision are going to try and turn the video game industry into a beast like hollywood or the music industry. Then the industry will kill itself.

i have respect for all game companys valve is still by far my fave and if blizzard wanted to make money from it they would of done it already but thats what i think.

The circumstances are different for Alien Swarm. In classic Valve fashion, they hired the group while they were already making the mod (which is actually a remake of a mod made by the same team back in '04 for the unreal 2 engine). Valve decided to give the game away instead of selling it, probably because most of the work was already done.

For DOTA2 they hired the head dude who was behind the original game, then started to make the game.

I don't think DOTA2 will be free because it was in house from the start.

Edit:
From Wikipedia
Alien Swarm was announced in 2005, under the title of Alien Swarm: Infested, as a Source engine sequel to the original Unreal Tournament 2004 mod. However by late 2007 the development blog had stopped updating, leaving its status uncertain. In July 2010 with the announcement of Alien Swarm it was revealed that Valve had hired the team behind Alien Swarm, who had finished the mod between working on other Valve products such as Left 4 Dead and Portal 2.