When he's in the hospital and is forced to censor letters, Yossarian signed his "name" as "Washington Irving." Later in the book, Major Major does the same thing on official documents. What's the significance of this? Why Washington Irving?
Three of the most important reasons appear to be a) the fact that he was dead b) the fact that most of the bureaucrats evidently hadn't heard of him (based on the fact that CID men come looking for him) and c) the fact that he was a major literary figure.
Point a) is important to the irony - if Major Major signs his name with the name of a living person, it comes back for him to sign again. If he signs it with the name of a dead person, it doesn't come back.
To some extent, it also likely symbolizes the soul-crushing effects of the bureaucracy. Yossarian and Major Major are simply taking the next logical step of signing their name as someone who's already dead.
This is actually kind of like the running gag with T. S. Eliot that Ex-PFC Wintergreen started.