Moore definitely named the station, however he was a vacant landowner who never lived on what was then only an outstation formed by an overseer and a few convict stockmen living in bark huts. If Moore's name was of Aboriginal origin, it would have been his overseer and assigned convicts who had the initial contact with the natives and later passed on the Aboriginal name for the area to Moore.
Baroness Gertrude Mary Denman (1884–1954)(bio here), the Australian Governor General's wife, named the new Federal Capital City of Australia "Canberra" on the 12th of March 1913 (post here). The resplendent ceremony conducted on Kurrajong Hill (Capital Hill) officially named the new city after the local Aboriginal name for the Limestone Plains "Canberry" meaning "meeting place" and hence, the subsequently named sheep station of Joshua John Moore.
Public acceptance of the official explanation was varied however:
The Sydney Morning Herald - 26 April 1913
The Argus - 23 June 1920
The Sydney Morning Herald - 26 February 1934
The Argus - 6 August 1937
The Canberra Times - 17 January 1939
The Sydney Morning Herald - 27 November 1942
The Canberra Times 9 May 1945