What was the question for this implicit rationale, and corresponding answer?
The important part for answering this question is: Jesse Katsopolis (portrayed by John Stamos; the character's last name in season one was Cochran, but was changed reportedly due to John Stamos wanting his character to better reflect his Greek heritage) is Danny's brother-in-law, Pam's younger brother, husband of Rebecca Donaldson and father of twin sons Nicky and Alex.
 The answer: Cochran
The question: Jesse Katsopolis (portrayed by John Stamos; the character's last name in season one was Cochran, but was changed reportedly due to John Stamos wanting his character to better reflect his Greek heritage) is Danny's brother-in-law, Pam's younger brother, husband of Rebecca Donaldson and father of twin sons Nicky and Alex. Born Hermes Katsopolis (as revealed in the season five episode "The Legend of Ranger Joe"), he was named after his great-grandfather, who in turn is named after the Greek god of swiftness. However, he did not like his birth name, as other kids teased him for it; so when he was in kindergarten, he begged his parents to have his name changed to Jesse, thinking that one had to have a "cool name" to be in the in-crowd. As an adult, he was more confident with his true name, telling the girls about the Greek god of speed, and how his great-grandfather saved a village from a volcano, but still goes by Jesse.

Answer this question: what was uncle jesse's original last name on full house?