In the Hellenized world, the Jews tended to replace their Hebrew names with Greek names that sounded similar.
Hence many called themselves Iason, like the Jason of Classical mythology, rather than Iesous, perhaps to avoid the opprobrium of belonging to the sect of Jesus.
Since the use of the name Jason dates back to pre-Christian times, then a such embarrassment of calling themselves 'Iesous' (note: in Greek) had to be equally pre-Christian.
First you carefully qualify with 'perhaps', and then in the very next line you strategically drop the qualifying pretext of 'perhaps'. Aside from that, your consistent abuse of sound deductive logic/reasoning never fails to 'rather' befuddle me.