About 大本営... Technically speaking, the official English translation of the kanji is "Imperial General Headquarters", and the kanji literally translate to "Great Headquarters", but given that KanColle is heavily implied to take place in contemporary times (e.g. the 2nd decade of the 21st-century) and that there's lack of any explicit references to Japan having either revived its Imperial days or having never had its Imperial government removed in the aftermath WW2, the use of Imperial-era terminology is possibly just the modern Japanese government/MSDF's attempt to ease the shipgirls' acclimation to modern times. Combining that with the absence of any kanji in the name that could remotely be construed as translatable to "Imperial", we could drop "Imperial" from the translation of 大本営 and render it simply as "General Headquarters".
Admiral, about my marriage with Kisaragi-chan...Call me up for the wedding ceremony, 'kay~Is this General Headquarters? U-umm, this is Mutsuki. I'd like to consult about my marriage with Kisaragi-chan...Approved.EEEEEH!?WHY ARE YOU SO LOOKING FORWARD TO IT, NYASHI!!THE HQ IS WAY TOO LAID-BAAAAAACK!!Our married life starts here!I don't think the higher-ups would authorize marriage between destroyers.Mutsuki-cha... or should I say, my dear ♡Hold on, are those papers legitimate?!