It is also occasionally referred to as "仲秋の名月," since August of the old calendar is right in the middle of fall (from July to September) and is called "仲秋," but "中秋" indicates August 15th of the old calendar and "仲秋" indicates the middle period when separating fall into three, so "中秋の名月" is the correct expression.
また、旧暦8月は、秋（7月から9月）のちょうど中頃なので「仲秋」と呼ぶため「仲秋の名月（ちゅうしゅうのめいげつ）」と表記する場合もあるが、「中秋」は旧暦8月15日をさし、「仲秋」は秋を三つに区分したときの真ん中の期間をさす言葉であるので、「中秋の名月」が正しい表記である。