Josephus is reported as the only one to mention the name Jesus, others merely mention Christus which means "The Annointed One".
The only person to physically annoint Jesus was Mary Magdalene.
With regard to Josephus here's the current thought. Josephus is the only commentator worth discussing here, although some Roman sources mention Jehosoah The Nazorean which could be Jesus.
According to Professor Paul Maier Scholars fall into three main camps regarding the writings of Josephus. On the first and longer paragraph on Jesus (18:63) which occurs amid events during Pilate's administration: 1) it is entirely authentic; 2) it is entirely a Christian forgery; or 3) it contains Christian interpolations in what was Josephus' authentic material about Jesus.
The first option, held by very few, would seem hopeless: no Jew (Josephus was a Jew) could have claimed Jesus as the Messiah who rose from the dead without himself converting to Christianity, and Josephus did not convert to Christianity. The second position, popular in late nineteenth-century skeptical scholarship, has some minor current support. A large majority of scholars today, however, share the third position, particularly in view of the newly-discovered Agapian text which shows no signs of interpolation.
75% of current scholars feel that Josephus did actually write something about the historical Jesus, even though the text of Agapius do in fact show two versions of the Jewish Antiquities.
All other commentators are merely responding to the Christian faith in their own way.