so Itachi and Kisame's names can kinda match

Like most characters outside Kiri, Itachi's name is written with katakana rather than kanji for weasel 鼬. But in Japanese, tiger sharks are called weasel sharks - itachizame (鼬鮫), with the first kanji from the meaning of Itachi's name and the second from Kisame's. While they're from a different family, another kind of tiger shark comes up in their meeting, as the description of shark pups devouring each other in the womb matches the otherwise docile sand tiger sharks.

And then there's Kisame's given name. While the kanji used are for demon shark, using different kanji, 樹雨 'kisame' is a noun. It's used for when fog settles around tree leaves and falls like rain. So a Mist Ninja finding their place alongside Leaf Ninja through the Rain Village/Akatsuki is literally summed up in his name

While being the only team to share ring placement and nail polish colour, the kanji on them, Vermilion and South, also match. Many of the Akatsuki rings are connected to heavenly beings in some way, but Itachi's, Konan's, and Deidara's are part of a set of Four Auspicious beasts - The Vermilion Bird, the White Tiger, and the Azure Dragon. They're all linked to different elements/weather/etc, tying the two of them together, as the Vermilion Bird is the deity of the south. Each of the symbols also has different phases of the moon connected to them, called mansions; one of them for the Vermilion Bird is 鬼, the first kanji in Kisame's name. And the main occurrence of the south kanji in the series is the Uchiha's Naka Shrine and Naka River; 'The Shrine/River of Southern Joy'. Itachi's Mangekyo Sharingan activates at the river, the tablet describing Infinite Tsukuyomi is in the shrine, and they meet by a seaside shrine.