I think the reading "Hassaku" comes from 八朔 which is the first day of August in the lunar calendar (I think), which is a special day for festivities praying for a good harvest. It is also the name of a citrus fruit grown in Hiroshima (probably because it ripens around that period?).
"Hozumi" I have read somewhere that it probably comes from 穂+摘む , meaning "picking ears" of rice, which probably started around lunar Aug. 1.
"Yazumi" I can only guess is a variation of "Hozumi" because the kanji 八 can be read "ya".
There are books on the history of Japanese names if you go to Japanese bookstores, but I've never read them. From what I know, some are aristocratic names linked to the Imperial family, some are of samurai origin, and many are names derived from geographical locations and localities, such as names of regions or descriptions like "middle of rice field," "on the sunny side of a certain mountain," etc.
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