What is the name of the state premier or darwin?

The answer above me is partly correct, except that the Chief Minister is not appointed by the administrator, they are the leader of which party which is in power, which unfortunately at the moment is ALP. Chief Ministers name is Clare Magela Martin she is chief minsiter. The leader of the opposition is Jodeen Carney and she would be chief minister if her party (the Country Liberal PArty) gets elected. The leader of each party is voted for by the members of parliament which belong to that party.

what????

I assume that you mean who is the premier of the Northern Territory. Because the NT it is a territory and not a state, there is no premier. However the Chief Minister (ie the head of the NT government) of the Northern Territory is The Honourable Clare Martin MLA.

In Australia, a Chief Minister is the head of government of a self-governing territory, while the head of government of a state is a Premier.

The Chief Minister is appointed by the Administrator of the Northern Territory, who in normal circumstances will appoint the head of whatever party holds the majority of seats in the legislature of the territory (in the Northern Territory, the Legislative Assembly). However, in times of constitutional crisis the Administrator can appoint someone else as Chief Minister.
Hope this helps.