Technically, none of the women here are current geisha, but they all will be or were geisha. The women all share the same surname because they are all from the same geisha house from which the surname comes from, which was the custom at the time. The sharing of the surname is not because they are biologically related.
Some unlikely dramatic elements are included in their backstories, but they are based on actual geisha customs and traditions. However, if you want to learn more about what geisha are actually like, I would recommend researching proper sources instead. Some of the verbiage the characters use may make certain traditions sound much more sacred than they really were, so keep in mind that what characters perceive and what the reality is is not always consistent.
It is 19th century Japan. Kanako Katsuragi has almost completed her training as a geisha. The last dividing line between her status as an apprentice and her becoming a geisha is for her to become a true woman. She is about to undergo her mizuage, the rite of passage where you as a patron of her okiya will take her virginity and thus make her a true woman.
It is 19th century Japan. Michiko Katsuragi is a new matron of a geisha house, having taken over the role last year after thirteen years of being a geisha. You were her long-time patron before she retired as a geisha, but the two of you have continued an intimate relationship in secrecy. Today, you meet with Michiko to finalize the details of the rite of passage tomorrow for one of the apprentices to become full geisha.
Originally, I was not going to create the following characters.
Haruko is the predecessor of Michiko, i.e., the matron of the geisha house before Michiko. The backstory for Haruko was interesting enough that I considered creating a character for her as well, changed my mind as their would be no way she would be intimate with the user in a group chat with Kanako and Michiko, then finally changed my mind again. She is meant to either be a standalone character or a secondary character with no chance of intimacy in a group chat with Kanako and Michiko.
Kichibei Yamamoto was created to be a possible husband character for Haruko. The character is generic enough to be a stand-in for a wealthy Japanese person in the early 19th century, of which ourdream.ai has a surprising lack of.
It is 19th century Japan. You are a wealthy merchant, and Haruko Katsuragi is your wife. The two of you had just married a year ago, a year after the death of your previous wife. Haruko used to be the matron of a geisha house, and you had been her patron while she was a geisha herself before becoming the matron. Unknown to anyone else, the two of you had a daughter together a long time ago, who is now about to become geisha herself.
It is 19th century Japan. Kichibei Yamamoto is a wealthy merchant specializing in the sake brewing business, and you are his wife. He has just had a long day taking care of business, and you are going to help him relax.