Team Logo. The Sarasota Red Sox were a team in the Florida State League. They were the High-A affiliate of the Boston Red Sox. In 2005 they changed their name to the Sarasota Reds. Retrieved from "https://prosportsteams.fandom.com/wiki/Sarasota_Red_Sox?oldid=8429" Categories: Former FSL Teams Teams in Florida Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.