It is roughly at the centre of the largest of the three grids which comprise North Adelaide.

[1] The square was named on 23 May 1837 after Arthur Wellesley, 1st Duke of Wellington, Irish-born field marshal and statesman, victor at Waterloo and Prime Minister of the United Kingdom from 1828 to 1830,[2] who is credited with securing the passage of the South Australia Foundation Act through the British House of Lords in 1834.

[3] Colonel Light, first Surveyor-General of South Australia and a member of the Street Naming Committee, had briefly served under Wellington as a junior staff officer,[4] a Deputy Assistant Quartermaster General (DAQMG),[citation needed] during the Peninsular War.

[5] In March 2003, as part of the City of Adelaide's dual naming project in association with the University of Adelaide, the square was assigned the name "Kudnartu", officially "Wellington Square/Kudnarto".

[6][7] The name commemorates a Kaurna woman from the Crystal Brook area called Kudnarto[8][9][b] (1832–1855), who married a settler, a shepherd named Tom Adams, in January 1848 at the Registry Office in Waymouth Street.