Team Logo. The Daytona Cubs were a team in the Florida State League. They were the High-A affiliate of the Chicago Cubs. In 2015 they changed their name to the Daytona Tortugas. Retrieved from "https://prosportsteams.fandom.com/wiki/Daytona_Cubs?oldid=13362" Categories: Former FSL Teams Teams in Florida Community content is available under CC-BY-SA unless otherwise noted.