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I'd like to preface saying I'm not an authority on this, I don't know a great deal about Korean names at all.

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However, I was able to find this name written as 애자 in Korean Hangul as a character in a Korean TV series.

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https://ko.wikipedia.org/wiki/%EC%95%A0%EC%9E%90_%EC%96%B8%EB%8B%88_%EB%AF%BC%EC%9E%90

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자 does indeed mean child via Korean Hanja 子, which was fashionable in Korean during Japanese occupation due to 子 being a common ending in Japanese names.

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Keeping on that track, 애 is listed as a possible reading for 愛 meaning "love".
https://en.wiktionary.org/wiki/%EC%95%A0

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Effectively, I believe this could be a Korean cognate of Aiko, in any of its forms. For it possibly meaning "beautiful child", that might be a possibility, as a less common way to spell Aiko in Japanese kanji could be 娃子. 娃, when used as a character in Japanese names, can mean "beautiful".

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https://b-name.jp/%E8%B5%A4%E3%81%A1%E3%82%83%E3%82%93%E5%90%8D%E5%89%8D%E8%BE%9E%E5%85%B8/f/%E5%A8%83%E5%AD%90/?id=162969

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https://en.wiktionary.org/wiki/%E5%A8%83

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I'm not well versed in Korean names as I said, nor Japanese names, so someone correct me if I'm wrong.