Of course Guerrero doesn't care about someone knowing his real name; for all intents and purposes that person is just a cipher, Guerrero is the one that matters. At the same time, using his legal name such that there's a paper trail (which he specifically states when talking to Ilsa) -is- something he cares about to prevent any one from finding his kid. Said kid is also the reason why the seemingly mythical Guerrero has a file at the CIA (remember, before the series, he was like Chance - a hitman that leaves no trace). Since his kid is the only true constant in his life, the company would be able to use that to track him down. Lastly, why use a car bomb to kill the rogue CIA agent? After all, he'd already beaten up the guy and had him at his mercy; it's not like Guerrero is squeamish. Because they smashed up the Eldo.
That's cool how everyone fears Guerrero as if he were Death itself. Until you realize that in order for that to happen, Guerrero must really have gone through with ... business ... for his presence to be a legitimate threat.