Cockburn was born in Kent Town, South Australia, a son of George and Mary Cockburn . He was educated at Flinders StreetState school, and joined the Register as a "library boy" around 1892, and was elevated to the literary staff, where he was rated "one of the best journalists in Australia" and "the smartest journalist of his years, column-crowding the dailies", before he was made an "excellent sub-editor" When in July 1914 the Peake government decided to institute a South Australian Hansard office, a function which had previously been contracted to the local press, Cockburn was selected assistant to Fred Johns's leader. He served in that position for eighteen years, until forced by ill-health to retire. Cockburn was admirably suited to the job, as he was noted for his speedy and accurate shorthand. Johns remembered his "bright and breezy nature, and sparkling wit and humor" somewhat offset by "temperamental faults — and who hasn't them". The work entailed not only recording the proceedings of the two houses of Parliament, but also of the various committees, notably the Public Works committee. Nevertheless, the position clearly allowed of time and facilities to pursue private research, as Johns produced a huge number of concise biographies of notable Australians which became a series of reference books, and Cockburn the voluminous notes on the histories of South Australian towns and geographical features, and the ensuing work for which he is remembered today, the manuscript of which the Mitchell Library acquired in 1936, and which was used by Stewart Cockburn for a new edition of his famous father's work entitled What's in a Name. In August 1916, at the height of World War I anti-German sentiment, Cockburn was appointed to the South Australian Nomenclature Committee, which was given the hugely popular task of expunging place names of Teutonic origin or association from the State's map. Their deliberations resulted in the Nomenclature Act of 1917 and their consequent wholesale replacement.
Other interests
In his younger days he was a member of the North Adelaide Cycling Club. He was also a lacrosse player and official, serving as secretary of the South Australian Lacrosse Association for several years. He was the organising chairman for a South Australian tour by the Canadian lacrosse team. He has been mentioned as reporting lacrosse activities for The Register under the pen-name "Canadia".
Family
Rodney Cockburn married Marguerite Elizabeth Stapleton "Reta" Guerin on 15 October 1910. Reta was a daughter of well-known accountant Herbert Robin Guerin, an AEI alumnus. He married again, to Ruby Ethel Adams Farmer on 1920. They had one son:
Stewart Cockburn
Alexander "Fid" Cockburn, Isabella Cockburn, George Stewart Cockburn, James Ralph Cockburn, Mary Cockburn, Walter Cockburn, and Margaret "Maggie" Cockburn were siblings.
Criticism
Cockburn's book Nomenclature of South Australia is not faultless, far from it. Geoff Manning, in the preface to Place Names of Our Land, the latest edition of his Romance of Place Names of South Australia, points out that apart from numerous omissions, something like one in ten entries contains errors of fact, some of them egregious. He is also critical of two pioneering toponymy historians, the surveyors C. H. Harris and H. C. Talbot who, when documented evidence was not available, published hearsay as fact. Information from these sources has been accepted uncritically by later historians, perpetuating many errors.