Why did Costigan use his real name while undercover, and not a fake ID?
Basically Costigan had to do enough jail time to convince the mob he was not a cop, because the Quinan could not conceal the fact that he was a police trainee, as Quinan said. And Costello and his men called him by his real name. He even turned to his cousin as part of his undercover method of operation.
But why not just have a fake ID and fake name? That way, no one would have known that Costigan went to police school at all. I mean don't most undercover cops take on fake identity's like Donnie Brasco, which was not the man's real identity?