Akebono(「曙」, Daybreak) doesn't have the same kanji as Akemi/Akatsuki (「暁」, Dawn) though, despite starting with "Ake".
Sure, both Akatsuki and Akebono have similar meanings (which is why they are sometimes paired together, like in Shino's Shitty Admiral series), but so are a lot of the destroyers (Two Beach Winds [One's rocky and the other sandy], Snowy Wind and Blizzard, etc.), and we do differentiate them even when providing the literal meanings of their names.