Yakuza, while definitely a Japanese organization - there were a population of Koreans in Japan from the feudal times forward, and a good amount of yakuza were actually Korean. The yakuza, while certainly a criminal syndicate, were the official representatives for the unguilded vendors and street peddlars, that lacked the protections that a "guilded" profession maintains. And they served as the police force inside the redlight/theater districts of urban areas - while samurai certainly enjoyed the entertainments, to serve as a police force for them - it was beneath them to do. The yakuza during every festival, rope pulled the huge taiko drums, and the shrine based "floats", something they did with honor. Because yakuza were considered "managers" of their districts, they were legally allowed to bear a single sword. The tatts, became a thing, because in feudal times, by Shogun decree, criminals were marked with a ring tattoo on their arms right above their elbows, each time they went to prison, so when looking for usual suspects, the samurai cops just pulled up their sleeves to find them. So the yakuza took their forced tattoos to the next level, and why it's their thing. But tatts worn by monks - no way, tattoos are waaay taboo in Japan, only yakuza wear them. I had a tattooist wizard archetype that served the yakuza.
Oh, and the finger cutting, self mutilation punishments forced onto problem yakuza members was about cutting off your pinkie, because your pinkie controls the movement of your sword, while the other fingers/thumb hold the sword - losing your pinkie, takes away combat effectiveness. You don't lose a second finger in your second "incident", though, they just kill you.
Yakuza meant "good for nothing", a losing hand in a card game with the result of 8, 9, 3 (ya ku za - 8, 9, 3 in one of the counting systems)
In modern Japan, their world famous tattoo artists aren't allowed to have public shops, they operate from home studios and are not allowed signage, business cards, websites - it's word of mouth, as well as how to find them. It's that taboo in Japan, still - and the same in Korea. American fascination with tattoos give the Japanese heebie geebies. You're not allowed to use a public bath house if you wear a tattoo. Yakuza use private ones.