"Tsun" for Haruka, though he turned out to be genuinely more of a Kuudere.
"Senpai" or "Sweetie-pie" for Makoto, emphasizing his caring nature.
"Shota" for Nagisa, who has the typical Token (Male) Mini Moe physical aesthetic, if not as exaggerated as some; he's more or less a CloudCuckoolander, though.
"Pimp" Explanation Appeared to be waving to the fans, presumably girls, in the original commercial, and thus identified as a ladies' man. or "Cameron"Explanation Stands for came-here-for-the-girls-turned-gay for Rin.
"Megane" or "Glasses" for Rei when he was first revealed and most were still more comfortable using the nicknames because the anime still had not aired.
"Far Left-kun" or "Far Left-kun 2.0" for Seijuurou due to his resemblance to Rei's prototype design.
The series itself is nicknamed "Swimbros!" or "Gay Swimming Anime."
Hilariously enough, if you simply put "free" into Google images, you get pictures of a red button with the word "free" written on it, but if you put in "gay swimming anime" pictures from the show come up, along with the anime Tsuritama.
"Anime Macklemore" for Goro, due to their similar look.
"Minishiba" for Momotarou, due to being Seijuuro's younger brother
The symbolic equation of Haruka=dolphin and Rin=shark is already established (promo art, Rin's teeth); and in the endtheme animation, as Haruka wanders through a desert wasteland, what does he pass the skeleton of? A Chinese river dolphin.
Dolphins and sharks don't exactly get on well in the animal kingdom. Then there's Makoto's orca...
What Could Have Been: This image◊ shows the Iwatobi Swim Club without Rei, but instead with another character named Kaede. Apparently this character would have been more easygoing than Rei, as well as retaining the "inexperienced newcomer" role Rei eventually got according to this interview.