Complex sentence: He got his nickname when the Pittsburgh fan base, mistakenly assumed the name "Mean Green" was Joe Greene's nickname; however, the wife of Coach Rust wanted to give a nickname to the team's outstanding defense.
Split into simpler sentences: He got his nickname when the Pittsburgh fan base, confused the name "Mean Green" as Joe Greene's nickname. Actually, the wife of Coach Rust wanted to give a nickname to the team's outstanding defense.