Nee-san?

I thought Hibiki just calls her Akatsuki instead. And IIRC the rest of the 6thDesDiv are also on a first name yobisute basis (not that they have any other names) with each other, except for Inazuma who might use (name)-chan instead (reserving -san for the bigger ships).

Knowing Hibiki, I can see her doing it to mess with Akatsuki.