Lt Governor Hobson named the new settlement in honour of George Eden, 1st Earl of Auckland.
In reference to the above - William Eden (hence mount Eden) who was from Bishop Auckland in the UK .
The actual word Auckland has 3 possible origins, all dating back a millennium.
(1) old Celtic river name with the last four letters denoting a cliff = Alclit = a river in the region (in UK) which later was named Gaunless which is a Norse word meaning 'useless' reflecting it's inability to power a mill, sustain fish or floodplains
(2) derives from old Norse Aukland meaning 'additional land' granted to the local Bishop by King Canute in 1020 (in UK)
(3) A derivative of 'Oakland' relating to surrounding forests in the area at the time (in UK)