Chinese characters(十六夜) mean sixteenth night. And 十六夜 as a word is “the sixteenth night of a lunar month”.
But “Izayoi” has another mean. “Izayoi” originated from a verb “izayou”. “Izayou” means “hesitate”. The moon after full moon rises a little bit later than the full moon, as if after some hesitation.
I took a picture of 十六夜の月. Like this.