The ancient Japanese name for July is written as 「文月」and it’s called “Fumizuki/Fuzuki.” The origin of the name is often said that it came along with a famous July event, Star Festival “Tanabata” when people write their wishes on a slip of paper to hang up on bamboo trees. Back then, people had the same tradition but to write short poems or songs on a slip of paper for the bamboo tree wishing their writings would get better. The character of 「文」has meanings deeply related to words such as a letter 「文字」 or a literature「文学」.
Tanabata is now well known as a summer event, but it was brought into Japan from China during Nara period. So the history of being named Fumizuki could have been one of the several fairytales like those of other 6 names so far. Other possible Japanese names for July are 「含み月」”Fukumizuki” and 「穂含み月」”Hofukumizuki” for it is the month when the rice grains start growing. Considering the cases of other months, nature and farming related origin seem to fit in right for the July’s Japanese name.
August is called “Hazuki” as the ancient Japanese name. Literally, it is related to leaves. As I have explained before, the ancient Japanese names for months are based on the lunar calendar and there is a slight time gap, about a month and a half, between the new calendars we use in recent day. It may be correct to assume the month of Hazuki initially indicated the mid-September, when the leaves are expected to start turning colors and fall on the ground around this time of the early autumn. That’s why September is called as「葉落ち月」“Haochizuki” or 「葉月」 “Hazuki.”