Never had a name had so much power literally and metaphorically speaking, not at least in saezuru. We only hear "Chikara" from Doumeki's own mouth while answering Yashiro's interrogation at the beginning of this story and from his mother while visiting him in the hospital when the first arc ends, so it only remains to think how close Doumeki and they can become that woman so she can call him the same. For this reason it is not uncommon for Yashiro to be so surprised and jealousy to break out within him.
The first theory of someone who does not know this story in depth would be to believe that both have maintained a loving relationship during these 4 years and that Doumeki has calmed his basic needs while waiting to meet Yashiro again, but someone who has really read what happens in saezuru can't believe in such a basic idea at least I don't. Doumeki told Yashiro "I want this body not to want anyone else", this phrase speaks of exclusivity and I can't imagine him asking for something that even he can't fulfill, on the contrary, I think he makes the request because it's his way of seeing love with Yashiro, he does not want him to be with anyone else and in his heart there is no room for another person so much so that he covers his hands with gloves at the precise moment that he begins his new life as a yakuza declaring: I am here but my feelings they will be preserved until the time when Yashiro returns to my life but let's leave the story of the gloves for another time.
An important detail that makes me curious is why in the scene where Doumeki enters the woman's apartment Yoneda leaves Inami's dialogue: "As always, you don't stop", is it perhaps a clue to tell us that in the same way as Yashiro he gets turned on by no one but Doumeki himself, he is still powerless and only Yashiro can turn him on. If the above is correct, the romance with the woman would be completely ruled out.
So if we eliminate the idea of a romance between the two, I can only think about the importance of this woman as an informant. Mama-san owns a bar where yakuza people usually meet to have fun, close deals, etc. therefore it is not uncommon for you to have important first-hand information to use at your convenience. Now, but where this closeness between the two comes from, the only clue we could have is the concept that Yoneda delivers through the conversation that Kamiya has with Yashiro in the bathroom of the Sakuraika house where he clearly explains what the intentions of the "women of the night", the protection of a man. Doumeki has not forgotten what he learned at the police academy and knows that information and contacts are pure gold, especially in the world of the mafia, he is also the "problem solver" assigned to that bar, that means he protects those who work there then it is ultimately a win-win relationship: information for protection.
Don't think that I have these thoughts to defend Doumeki with a romantic ideal, of course not, because if Yashiro could continue looking for other men in these 4 years then why couldn't Doumeki take refuge in someone too. It's just that to me the character's devotion to staying in the yakuza for love and putting this whole plan together for all this time doesn't fit with there now being a third person in the story.
On the other hand, what happens to Yashiro when he hears the name of Doumeki from this woman is a ticking time bomb. Yashiro has a theme with women that Yoneda is always developing throughout the manga, from his earliest childhood the most important woman in his life abandoned him to his fate with his stepfather, then in adolescence he realized his masochism by to have sex with a girl and from that moment he began to frequent places where yakuzas met to obtain the violence that aroused him, but many times these same men reminded him that his destiny would have been different if he were a woman.
Ryuzaki mentions that if he had been a woman he would have been able to protect him, Misumi tells him that it reminds him of his wife, the man with whom he has a relationship in his early years in the yakuza and who is expelled because of him, constantly treats him like a girl and all this blows up Yashiro. But when Yashiro and Kamiya have a conversation in the bathroom of the Sakuraika's house, Yashiro realizes that in the world of the yakuza women still need a man to protect them and it seems to me that for a moment he thought that if he had been a woman as everyone told him, now he would be without so many problems with Doumeki.
Yashiro has all this going around in his head and when he sees the closeness that Doumeki and mama-san have, it's obvious that everything fits and his jealousy explodes. I can't leave out the scene from this last chapter when everyone is eating in the restaurant and Kamiya makes Doumeki see how gentle he is with women, to which Doumeki replies: "I can be gentle with Kamiya too." This for Yashiro is the straw that breaks the camel's back, the kindness to mama-san, the kindness to women, the kindness to Kamiya and the kindness that Yashiro craves so much, where is he?
Yashiro no longer imagines men raping him in a group, now he dreams of Doumeki chasing him, kissing him and letting him lie on his legs like in the past, that's what Yashiro wants at this point in his life, but he believes that everything that is held by other people close to Doumeki. The place that Yashiro occupied in Doumeki's life is no longer even as his boss, from the moment they met again after these 4 years Yashiro has realized how much he lost and how much he wants to get it back, that's why he goes out on he looks for Kido to self-sabotage again and run away from what is happening to him with Doumeki.
This chapter focused on jealousy and how much damage it can do to us, they say that a person can hide any feeling except when they are jealous and it became clear that neither Yashiro nor Doumeki can run away from this feeling anymore.
If there are errors in the text, it's Google's fault hahaha I'm sorry but I hope it's understood. Thanks for reading my ramblings.