Warringah's an aboriginal name that's describes the northern area in the team's local area, Manly being the smaller. more densely populated southern area. According to Wikipedia there are various meanings for Warringah including "sign of rain", "across the waves" and "sea". It was once the home of the Guringai (or Kuringgai) language group of the Garigal clan, who owned the land between Port Jackson and Broken Bay, extending to the Lane Cove River in the west.
Manly was the name given by Captain Arthur Phillip upon seeing the indigenous people "their confidence and manly behaviour made me give the name of Manly Cove to this place".