KMT put the K in Kaohsiung, before the KMT occupation, the place was always called Takao. It was called Takao by the local Aboriginals, and the Dutch recorded it as such back in 1624.
Early Holo immigrants transliterated it to 打狗 (tánn-káu). The Japanese transliterated it to 高雄 which is an existing Japanese location name, pronounced as Taka-o.
It was the KMT who insisted calling Kaohsiung based on the Mandarin reading of the Japanese transliteration.
If they even bothered to learn about Taiwan's history, or have a tiny bit of respect for the locals, they would have renamed the place to 大高, thus keep the city's name the same as before in both Mandarin, Taigi, and Hakka.