The name means new moon of autumn. Hatsuzuki was an Akizuki-class destroyer built at Maizuru Naval Arsenal. She was laid down on 25 July 1941, launched on 3 April 1942 and completed on 29 December 1942.
In 1943 she was a Truk-based fleet escort. She sailed with cruisers and carriers to Kavieng and Rabaul and back, and screened fleet sorties to Eniwetok and Truk. On 3 April 1943 she helped fight fires aboard the bombed cruiser Aoba at Kavieng. In January 1944 she helped tow the torpedoed Suzutsuki into Kure. In the Battle of the Philippine Sea on 19 and 20 June 1944 she escorted Ozawa's Force A, assisted the torpedoed Taiho and helped rescue survivors.
On 25 October 1944 she sailed with the Northern Force. In the Battle off Cape Engano she stayed behind to cover the rescue of Zuikaku and Zuiho survivors by Wakatsuki and Kuwa. An American cruiser-destroyer group found her, and she fought it for about two hours before she sank, east-northeast of Cape Engano. Eight of her crew and 17 Zuikaku survivors in a cutter lowered before the last fight lived; the cutter reached southern Formosa on 14 November after 21 days. Otherwise she was lost with all hands, including Captain Shigetaka Amano, commander of Destroyer Division 61.
Commanding officers, from the combinedfleet.com record: Commander Shooichi Taguchi, 29 December 1942 to 1 August 1944; Commander Kanematsu Hashimoto, from 1 August 1944.
Sources: Allyn Nevitt's combinedfleet.com Tabular Record of Movement for IJN Hatsuzuki; Wikipedia, Japanese destroyer Hatsuzuki, rewritten here.