I don’t think Jesus lent his name or it would be called Jesusism. And from my reading and understanding I don’t think Jesus would recognize the religion that people now call Christianity(or the way some people use it. We only have the word of someone who said Jesus said or did something, so there is a lot of confusion about what a Christian is today.
Jesus is a not accounted for having existed by any archeologial evidence, he was first written about some 60 years after they said he was around and all the stories were similar to popular lore by a guywho started his own group, a few decades later a formal religion came into being and added stuff while removing what they didnt like and so on with kings and popes modifying to suit their needs along the way. There is no evidence historically of jesus other than a history of people writing about him that clearly could not have been alive while he was supposed to have been alive.
I am in agreement with you, It is taking the word of who ever wrote about him,since it is quoted that he only wrote in the sand, we cannot know if Jesus said or wrote anything,or prove he existed, although most historians feel that there was a man named Jesus who had followers.