The man’s name was jesus – just a name. using the other part together with it that means in Greek “anointed one” gives him a title, and that could be construed as a recognition of the way in which they regarded him contrary to Torah, and therefore should not be used. The historicity of this man is still in dispute, and even in our own traditions there is machlokes if he was the same yeshu who the Gemara wrote about or if that one lived a couple of generations earlier. not pashut. The book that was a collection of all Jewish traditions about him, called Sefer Toldos Yeshu, included every story, anecdote and legend about him and his followers, embellished as generations went by and his followers (or more accurately, the followers of the meshumad Paul, who is the biggest villain in all of this) became more powerful and more cruel, does not exist anymore and is only known through quotes and excerpts.
As far as the greeting goes, I don’t get too exercised about it. People are genuinely making an effort (for the most part) to be a bit kinder or friendlier around this time. I’m not going to make a scene of Jewish entitlement by expecting their friendliness to conform to my worldview, and I won’t give them a greeting in return that is meaningless to them.