One of Wragge's chief claims to fame is that he is the first person to introduce the systematic naming of storms and cyclones, choosing feminine names, particularly those of South Sea Islanders for which he had an abiding admiration, for tropical storms and for unpleasant southern storms often using the names of politicians who thwarted his ambitions or denied him funding. He advocates his naming system for tropical storms in a lecture quoted in his 1901 almanac:

Special mention was made to the disturbances named ‘Eline’ and ‘Luita’, and to the fact that he was the first meteorologist to adopt the system of giving names to storms, in order that those who might experience any storm might more readily associate their experiences of the storms by reason of their names. He was thus able to serve the public in a domestic manner. In his general daily remarks, which were framed in a pleasant readable style in order to induce the people to take a more vital and real interest in their own Weather Bureau, he had recommended parents of infant daughters to forsake for the time the stereotyped ‘Susan’, ‘Jane’, ‘Eliza’ and ‘Anne’, and to substitute therefore the names of the tropical hurricanes, which are called by the mellifluous appellations of the soft eyed, dusky beauties of the South Sea Islands, savouring of the taro patch, the palm grove, and the coral reef. In this he had succeeded, and when he was in the suburban trains, going to his residence from the city, people accosted him with the pleasing information that they had increases in the family, and had named their daughters ‘Eline’, ‘Luita’, ‘Leala’, &c.

Wragge's career in Australia ultimately ended in disappointment as he was overlooked for the leadership of the new Commonwealth Meteorological Bureau for the establishment of which he had been a vocal advocate. Wragge was still railing against unsympathetic politicians and giving their names to the most unpleasant weather when, in July 1903, lack of support forced him to close the Central Weather Bureau. He then spent most of his life on lecture tours, mainly outside Australia, until in 1910 he made New Zealand his permanent home. He documented his travels in the Pacific in The Romance of the South Seas published in 1906 and including many photographs of the 'soft eyed, dusky beauties' that he was so fond of.