Aboriginal association with the Berrima area is considered to extend back 40000 years. At the time of European exploration of the district, the Gundungurra* peoples were inhabiting the location between Goulburn and Camden and their language gives many of the words for locations used today.

Berrima is considered to mean “southward” or possibly “black swan” (1)

Wingecarribee is “Winge Karrabee Karrabee” Winge for fire and Karrabee for wild, therefore meaning a place of “many wild fires” (2) or possibly “a flight of birds” or “waters to rest beside” (3)

*  Alternately known as Gundungurra, Gundungari, Gundanora, Gurragunga or Burragorang (1)

References
(1) https://en.wikipedia.org/wiki/Berrima,_New_South_Wales
(2) https://www.southernhighlandnews.com.au/story/2868745/indigenous-peoples-once-thrived-in-wingecarribee-district/
(3) https://economy.id.com.au/wingecarribee/about