Can Cony be used as an English name for women?

It should be no problem. It turns out that there are no Asian surnames in English names. Later, China and Asians immigrated to the United States or Europe and America in large numbers, leaving the surnames left by Asian ancestors unchanged. As long as your name can have a phonetic symbol or be read through a series of phonetic symbols, there is no problem. Your pronunciation can be considered as "Kouni", but if westerners are more intimate with women, especially with each other, they might as well change it to "conie" or "Kouni".