>> HaGaon Yosef HaBarrera HaShlishi [...]
>> (btw, literal translation is "The Exalted Genius Joseph The Barrera
> the Third").
> Which part means "the Third"?
"HaShlishi"
> and why the "Ha" prefixes?
It means "the".
> If I wanted to add my middle name (Samuel) would I stick a
> "HaSamuel" in the middle?
Only if you wanted to be The Samuel. Also, if you're willing to
accept "Yosef" for "Joseph", you should also substitute "Shmuel" for
"Samuel", in keeping with the return-to-tradition theme.