It is "id" software, no caps, no periods. It is named for this concept: http://en.wikipedia.org/wiki/Id,_ego_and_super-ego
I used to make similar mistakes years ago, for a long time thinking it was "Eye Dee Software", so I'm posting this to enlighten others, rather than being a grammar commie.
Interestingly, there was a game called iD published in 1986: http://en.wikipedia.org/wiki/ID_%28video_game%29