Sort of addressed this back in a couple of threads.
During the Japanese era, Tâi-uân-uē 台灣話 was used exclusively. The exonym was already in use in late Qing-governed period by Manchu officials referring to the language Tsiang-Tsuan language mixture. For speaker of Tsiang-Tsuan languages in Southern Fujian, Taiwan, the Philippines, and SEA, there wasn’t a name to refer to the language family collectively. Hoklo/Holo was also only a derogatory exonym used by the Hakka. Speakers just referred to their own language by the place of origin, like Tsuân-tsiu-uē, Tsiang-tsiu-uē, Amoy, Teochew, Lán-lâng-uē (Filipino), and so on.
You can see this in the names of Taigi dictionaries throughout history:
Since the Japanese period, Taigi and Taiuanue were continued to be use officially, as many early dictionaries published during early KMT-occupation still referred to the language as Tâi-uân-uē 台灣話 or Tâi-gí 台語.
Really, really, early on, like back in the 16th century, the Spanish wrote dictionaries such as the 1593 Doctrina Christiana en letra y lengua china, the 1604 Dictionarium Sino Hispanicum, and the 1626 Vocabulario de la Lengua Chio Chiu, referring to the version of Tsiang-tsuan language mixture in Taiwan and Manila as just Chinese.