What would Jesus have been called during his own time? My Middle Eastern professor once told me it would have been "Yeshua Bin Yusuf," or "Joshua son of Joseph." Is this accurate?
Yes it is accurate. His name was Yeshua which was Joshua.
Not exactly. All of these are transliterations from Hebrew, which has a completely different alphabet and it's own unique pronunciation. Also, it's generally agreed Jesus spoke Aramaic, so, if you want to go back in your time machine and start asking around for "Yeh-shoe-uh Bin You-suf" people will probably go "Huh?"...same as if you go to Mexico and ask for that guy "Gee-zuz" :)
In Aramaic, it's pronounced like "Ee-sho". Sort of like "Lee" without the "L" and "show".
See this page for an explanation and some audio of pronunciations. http://wahiduddin.net/words/jesus.htm