Some people seem to think his middle initial was H...
I'm not sure if they used middle names in that place in those days.
I don't think they used surnames, at least not for he ordinary class of people, and if not, then there would be no such thing as a middle name or a last name.
If identification beyond a given name was needed, many folks seem to have used their home town, as in "Jesus of Nazareth."
Occupations might also be used, like "Joseph the Carpenter" or "John the Baptist."
They also tacked on other identifiers, like "The Greater" or "The Less" or "The Fair."
It sort of reminds me of the present day Sherpa people, who don't use surnames. If they're doing something Western that requires it, like opening a bank account, they just use "Sherpa" as a last name, but they don't consider it a name; it's just something to fill a space on a form.
Names are only one of the ways we can get confused by trying to think in modern terms about ancient times. Not just customs but ways of looking at the world have changed. That makes the translation of ancient languages especially challenging.
One of the reasons Christianity has split into so many sects is that some people read the scriptures as if the were written in modern English, and they try to understand them accordingly; some are familiar with the languages they were written in, the concepts of the time, and the associated literary and speech conventions of the day; most folks stand somewhere between those extremes. You can see where different people with different degrees of knowledge and understanding might read the same passage and come up with wildly different interpretations of what it says and means.
My guess is that he didn't have a middle or last name in the sense that we do.
I think you are right.....