Complex sentence: Jesse's character was supposed to be named "Adam Cochran", but John Stamos insisted on his having his name changed to "Jesse Cochran" which later became "Jesse Katsopolis" for the rest of the show's run.
Split into simpler sentences: Jesse's character was supposed to be named "Adam Cochran", but John Stamos insisted on his having his name changed to "Jesse Cochran". Thus the name was changed to "Jesse Katsopolis" for the rest of the show's run.