He invented the name and the policy of making the members of this oddball religion stand out from the crowd with as many contrarian positions as possible.
That's the best explanation for stubbornly going against all the evidence to the contrary. The need to separate the group from the one powerful symbol that would link them to the other christian faiths.
I'd even venture that it would give too much of a focus on Jesus for the Borg's tastes. They want to keep their followers obssessed with the warrior god and his nasty judgement to come, all to keep up their operations.