If you plan to call it “Yueye”, then go with とう. For つきよ I’d go with しま.
しま
じま
Not because it’s on’yomi, but because the first one ends with ん, and the second one… because my gut says so.
That’s not kun’yomi, that’s Ainu - it’s a “foreign” name, hence とう. Kanji were chosen that approximate the Ainu reading.