Bear in mind that the earliest non-canonical christian writings do not give the name Jesus but call him Lord. The name "Jesus" certainly appears by the third quarter of the second century .......... to add a name or attribute a belief to a character was easy peasy--just make sure you destroy the earlier copies.
We have the Roman Catholic church at Emperor Constantine's urging to thank for the unification of all Christian (and pagan) cults under the name of Jesus in the fourth century. By then the idea that Jesus existed was not in doubt in the minds of the faithful. The poor people had no choice but to believe in authority.
HB is there any books that deal with this subject; that is that the name Jesus didn't appear till the second century? Thanks!