Well, Schützeninsel came first, as the city center of Prague used to be German historically. Then came the Czech translation into Střelecký ostrov. The English "Hunter's Island" would be a literal translation of the meaning as it was used by royals for their fox hunts. Hunter's Island is also used on spot by local tour guides.

It's not the English name, it's the german name. http://www.prague.eu/de/objekt/orte/518/schutzeninsel-strelecky-ostrov