Team Logo. The Greenville Swamp Rabbits are a team in the ECHL. They are the minor league affiliate of the New York Rangers. They get their name after the Swamp Rabbit Trail near the city. Retrieved from "https://prosportsteams.fandom.com/wiki/Greenville_Swamp_Rabbits?oldid=14679" Categories: ECHL teams Teams in South Carolina Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.