The Akatsuki-class wears a white and dark blue serafuku with a "III" somewhere on themselves as well as some form of black legwear. Inazuma herself has long brown hair in her signature folded ponytail and black kneehighs. The "III" is on her right kidney.
Inazuma historically collided with Miyuki, and a transport, and all the other warships that had also been named Inazuma (besides the most recent version, which is still in active service) have collided with another ship, leading her to be portrayed as often clumsy (and that she has a killer headbutt...).
Inazuma's name means "Lightning", so sometimes she is called "Den-chan", with "Den" being another name for lightning (and another reading of the Kanji). The same "Den" can be the first part of the Japanese word for "radar" (Dentan), so occasional puns are made about Inazuma being a radar, or being taken as a replacement for radar (see post #1661115).
She also has a dark persona sometimes called Plasma-Chan. This is a joke that originated in a comic (post #1917287) where an artist put his words of hatred for another artist named Nasu (whose name means "eggplant"). Depending on the artist, Inazuma might slip back and forth into Plasma-chan in various ways, from being an irrational response to eggplants, to being "Inazuma's serious side", to simply being an always-psychotic character among some artists with darker proclivities.
Several authors like to portray innocent Inazuma breaking down into the darker version due to a shitty admiral's incompetence or trolling. In such cases, her catchphrase sometimes becomes "nanoDEATH", and she takes on severely intimidating aura. This often overlaps significantly with Plasma-Chan.