The name was first used for a simple synth I developed in 24 hours at MusicHackDay Amsterdam in 2012. It could make some drone-ish fm sounds controlled via midi. Looking for a suitable name, I asked people at the table where I was hacking, and someone suggested Axolotl.
The animal is a wink to a few other species, the Chameleon and the Capybara.
I designed the logo myself (while I have no graphics design skills), using Eagle, a schematic/circuit board editor. Its limits (supporting only round-capped lines, polygons, arcs and circles) as graphical design software gives the logo its distinct look. The design is styled like an unusual component in an electronic schematic diagram. Yes, two inputs and 4 outputs does not reflect reality, but there is also midi, usb, sdcard etc, hard to represent it all...
This is how the "Vitruvian Axoloti" [wink] looks like:
Googl-ability was one reason: there was also "proce55ing" (versus processing), which used to be helpful when googling around, as including "processing" in a search query would give a lot of unrelated results.
Pronounce-ability was another reason, but I'm not quite sure it's effective.
Those reasons could be questioned or challenged but even if I'd want to change it, it'd be hard to change the whole internet.