The family name "Yossarian" indicates that this character's family heritage is Armenian. In many Slavic languages, including Armenian, the suffix "-ian" (sometimes spelled "yan") is found at the end of the name. It means "the son of;" one of the character's ancestors, whose name has become the family name for his successors, was the son of Yossa.
Pronunciation of the name would probably follow the usual pattern for Slavic names, with the accent on the second syllable of the name. The first syllable would feature a long "o" sound; the other vowels would sound as English speakers would expect for those combinations of letters - the "i" pronounced like a long "e" followed by a short "a" in the final syllable. Therefore, the full name would be pronounced "yo-sar-e-yan."