Many of the names in Dorohedoro mean something (ex: "Dokuga"="Poisonous Moth"), but I think "Ai"s names are the most fascinating since they play on each other. Some of his names are written in kanji, some in katakana, but they all have the sound "AI" in common: AI, kAI, AIkawa, cAIman, pAIman.
Ai
Ai, the original self, is present as the root of all his incarnations. In fact, "AI" is a homonym of "I," or essential identity.


This connection is also carried over to puns, such as the chapter title "Eye Contact," in which Haze sees Kai for the first time in years. The katakana script for "eye" phonetically spells out "AI" - doubling as both "Eye Contact" and "Ai Contact."
The name Caiman, aside from being a species of reptile, can also be thought of as a Kai-Man.


It was the Kai personality that originally became Caiman (he has crosses on his eyes until he remembered his other identity of Aikawa by visiting the Zagan school and switched heads).
Caiman
The English words Pie-Man are written as Pai-Man in Japanese phonetic script.
Pieman
Kai
Kai's name is written with the kanji for the verb "to break; to destroy; to demolish," which is... appropriate. XD
But the Aikawa name is probably the most interesting.


It is written in kanji, with the "ai" part as the symbol for the verb "to meet; to encounter," and the "kawa" part as the symbol for "river."


As such, it can mean "to meet at the river," specifically the drainage of toxic sludge that Ai dove into in order to become what he is now.
Aikawa

But Ai-Kawa can also be interpreted phonetically. "Ai" would represent the original Ai self, and "kawa" is the root of the verb "kawaru," which means "to take the place of; to substitute for; to take over for; to represent; to change places with; to switch," which is of course what "Ai"s aspects do with each other, and the Aikawa aspect in particular is the more PR representation that he uses to infiltrate the common world.

Another meaning of "kawa(ru)" is "to change; to be transformed; to be altered; to be different; to be uncommon; to be unusual." This interpretation of the name tells of how Ai transformed himself into a magic user (and then some), and also what a unique kind of creature he became.

(Why Nikaido also has "AI" in her name is yet to be determined.)
Darth Kai's Smoke
.
It's significant to note that Ai is the only person in
Dorohedoro with a last name: Coleman. While it could
have only been mentioned as a way to track down Ai's
relatives, there may also be a deeper meaning.

Through phonetic play on words, Coleman becomes
"Coal-man." Kai was most famous for inventing black
powder, which looks like powdered coal or ash. Haze
explicitly says so. Black powder was used to increase
a sorcerer's magic smoke output, amplifying abilities.

Of course, our burning of coal also creates
a ton of smoke. It's used as an energy source
on Earth, and magical smoke is likewise used
as an energy source in the sorcerer world. It
fuels their version of technology. Black powder
was fed into Ai's perfected bio-suit and, after
he put it on, it generated an extra-potent type of
black powder. The new body appears to run on this.

And so Ai Coleman = "I, Coal Man." The name
may be the seed of Ai's ideal or ultimate
self, and a foreshadowing of what he would
become: a being of perfected coal and smoke.
This suggests that the mask Caiman, Aikawa, and the four-headed coal creature wear is not a "gas" mask but a "coal" mask. The mask that coal miners wear looks nearly identical to a gas mask, though it is less well-known.
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DISCLAIMER: all story, art, characters are copyright Q Hayashida. This is a fansite. No copyright infringement is intended. Translations by Gantz Waiting Room, VIZ Media, and sometimes myself. Dorohedoro is published in Ikki Magazine.