Most Israelis know Josephus as the author of The Wars of the Jews (מלחמות היהודים, often mistranslated as The Jewish Wars)—a history of the Judeans’ revolts against foreign rule from the time of Seleucid to the beginning of the revolt against the Romans in the late 60s CE. As such, we’re grateful to him for the detailed information (which is sometimes the only source we have for some events), although there is suspicion that he was biased.
Fewer, I think, know that he was a military commander of the Jewish forces in the Galilee at the start of the revolt (“general” is perhaps over-egging it a bit). Some know that his Hebrew name was Yosef Ben-Matityahu.
Remarkably, fewer still know that his Roman name was not “Josephus Flavius”, but “Flavius Josephus” (actually, Titus Flavius Josephus): on becoming a Roman citizen, he adopted the emperor’s name “Flavius” as his nomen (clan name), but “Josephus” as his cognomen (family name within the clan). He could hardly have claimed Flavius as his cognomen.
(See this and other answers to this question at Quora.com)