If you are looking for the name of the Wandering Jew of folklore, his name is Ahasuerus, usually, but there are other variants.
I have never heard of him being associated with one guy who slapped Jesus. Jesus got slapped by a lot of people. The point of talking about That One Guy is that he was getting on Jesus for “showing disrespect” to the high priest, when really Jesus was speaking the literal truth, AND was the eternal High Priest, AND was king, prophet, Messiah, and God Himself. Sort of a dark humor moment.
Also, remember that a fair number of these minor Gospel characters are people we know about because they became Christian afterward, and were available to evangelists as eyewitnesses. They are not named to spare them embarrassment, as well as to keep the narrative flow moving. Of course, John was there at some of this stuff, but he knew a lot of these folks through his priestly connections. So it could be either way with this guy.