Not a joke, I don’t trust you, half-pint, I don’t trust Jeff from Today’s Special, I don’t trust Barold whatever his name– nobody, I trust nobody–nothing.
"Or is it like a Jerry/Gary situation where everybody calls him that, even their captain." Davenport is under the impression that it's his real name. That was part of the joke, convincing the captain that his last name was actually Bluejeans. They broke into the file room and changed all the records. Barry's given up on his actual name since he never really minded being called Bluejeans. By the time Shit Goes Down it's become more his name than his actual name so Lucretia lets him remember it.