Named after Dr Henry Norman Barnett, who lived nearby at Thornhill on Upper Newtownards Road. He was a specialist in ear, nose and throat medicine. Further biographical details are given in Knock, Knock... who was there? by Keith Haines (2014), pp. 58-66.
"that three streets in the added area off Newtownards Road be named 'Castlehill Road', 'Castleview Road', and 'Barnett's Road and that the works committee be requested to have these names erected an estimated cost of £1". (Minutes, Improvement Committee, 18th June 1901).
"That Dr H. Norman Barnett be informed in reply to his letter of 6th Inst. that this Committee do not see their way to alter the terms of their resolution of 19th April last, as to to completion of Barnett's Road". (17th May 1904).
"Read application from property owners and Residents in Barnett’s Road to have the name of that road changed to Ashley Road, and referred to the Surveyor to communicate with the owners of property requesting them to suggest a more suitable name and to have the application signed by all interested parties". ( 18th February 1908).
"Resolved – ...that the name Barnett’s Road be approved for a continuation of that thoroughfare on the property of Mr. McMaster". (7th May 1935).