"Ono-Sendai: in the book this is a Japanese corporation that manufactures cyberdecks. In Japanese “Ono” means ax and “Sendai” is the name of a prefecture in Japan."
Ono (斧) is indeed ax in Japanese, but is also a common surname. (The name is written differently, as 小野, no relation to axes.) Being a company name, it sounds more natural to interpret it as a surname rather than a weapon.
Non negligible possibility: the "ax" is also the traditionally identified root for labyrinth - 'labrys' intending the "double-edged axe", and "labyrinth" the "extended, intricate palace under the symbol for power".
This may suggest (were it intentional from Gibson) the "matrix" as a futuristic labyrinth under the same symbol of power. (You - presumably - accessed the labyrinth through a portal with the labrys, and you access the matrix through a portal with the "ono".)
Ono (斧) is indeed ax in Japanese, but is also a common surname. (The name is written differently, as 小野, no relation to axes.) Being a company name, it sounds more natural to interpret it as a surname rather than a weapon.