The main reason 2...c6 doesn't have a name is that it is almost entirely a transpositional tool.  For instance, if you play 3.Nc3, Black can switch to a Slav (3...d5!) or play 3...g6 4.e4 and if 5.Bg7 you also have 5.e5!?  This isn't covered in any books because the line gives White a fairly clear advantage without too much work.

You are much more likely to face 3.Nc3 g6 4.e4 d6 which still leaves White with an advantage after almost any reasonable move. Here are two possible transpositions after 4...d6:

5.Be2 Bg7 6.Bg5!? 0-0 7.Qd2!?(7.f4!?) a6 8.g4 b5 9.f3 h5 10.Rd1
and 

5.Be2 Bg7 6.Nf3! 0-0 7.0-0 (7.Bg5 is also fine for White.7.Be3 gives Black a small amount of counterplay by 7...Ng4) a6 (7...Nbd7 is met by the nasty 78.e5, which is why you don't see ...c6 very often at the highest levels) 8.e5! de5 9.Ne5 and already White has an advantage!  One game to look at is Cifuentes-Flear, 1988.


Of course, you can go your own way as White and play 3.d5 which should also lead to an advantage.

I know this isn't an entire book, but you get the idea.  White can reach an advantageous position compared to most KIDs simply by playing normal KID ideas which can be found in most books on the King's Indian.