Complex sentence: Following Lombardi's death in September 1970, the trophy was named the Vince Lombardi Trophy, and was the first awarded as such to the Baltimore Colts following their win in Super Bowl V in Miami.
Split into simpler sentences: Following Lombardi's death in September 1970, the trophy was named the Vince Lombardi Trophy. The first trophy awarded under the new name was presented to the Baltimore Colts following their win in Super Bowl V in Miami.