There isn't a direct, single Korean equivalent for the name "Kiki." Korean names are typically formed using hanja (Chinese characters) which are then romanized. Since "Kiki" isn't a traditional Korean name, you would need to choose hanja that sound similar or have a similar meaning to create a Korean spelling. This would result in multiple possibilities depending on the desired meaning and pronunciation.
Therefore, there's no single "correct" spelling. You would need to decide on a meaning or sound you like and then find appropriate hanja.